# Drawing Straight line graphs The gradient from Coordinates www.mathsrevision.com General Equation y = mx + c S4 Credit Equation from 2 Points Best – fitting.

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Drawing Straight line graphs The gradient from Coordinates www.mathsrevision.com General Equation y = mx + c S4 Credit Equation from 2 Points Best – fitting straight line Straight Line Graphs Modelling Situations The gradient Vertical ÷ Horizontal Exam Type Questions

11-May-15Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com Q1.Calculate 7 – 5 x 2 Q2.Calculate S4 Credit 9 8 5 Q3.Is this triangle right angled ? Explain

11-May-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 1.To show how to get the equations for horizontal and vertical lines. 1.Understand that vertical lines have equations of the form x = a The Gradient of a Line S4 Credit 2.Understand that horizontal lines have equations of the form y = a

0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 11-May-15Created by Mr. Lafferty Maths Dept x = y = Equations for Vertical and Horizontal lines Mark the points on your grid below and then join them together Vertical lines have equations of the form 8 Horizontal lines have equations of the form 2 x =-6 y =-9

11-May-15Created by Mr.Lafferty Maths Dept Now Try MIA Exercise 2.1 Ch7 (page 136) www.mathsrevision.com The Gradient S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com Q1.Write this number in full to 1 sig. figs Q2.Calculate the volume of the triangular prism. 12cm 8cm 20cm S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 2.Calculate simple gradients. 1.To explain how to calculate the gradient using a right angle triangle 1.Gradient is : change in vertical height divided by change in horizontal distance The Gradient of a Line S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com The Gradient Change in vertical height Change in horizontal distance The gradient is the measure of steepness of a line The steeper a line the bigger the gradient Difference in x -coordinates Difference in y -coordinates S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com The Gradient 3 4 3 2 5 2 6 3 S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept Now Try MIA Exercise 3.1 Ch7 (page 139) www.mathsrevision.com The Gradient S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com Q1.A house 4 years ago is valued at £50 000. Calculate it’s value if it has increased by 5%. Q2.Calculate 3.36 x 70 to 2 significant figures. Q3.Write down the 3 ways of factorising. S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 2.Calculate gradients given two coordinates. 1.To explain positive and negative gradients using coordinates. 1.Know gradient formula. The Gradient of a Line S4 Credit

m = gradient x1x1 11-May-15www.mathsrevision.com 13 y-axis O x-axis www.mathsrevision.com The gradient using coordinates x2x2 y2y2 y1y1 S4 Credit

m = gradient 11-May-15www.mathsrevision.com 14 y-axis O x-axis www.mathsrevision.com The gradient using coordinates Find the gradient of the line. S4 Credit

11-May-15www.mathsrevision.com 15 y-axis O x-axis The gradient using coordinates Find the gradient of the two lines. S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com The gradient formula is : It is a measure of how steep a line is A line sloping up from left to right is a positive gradient A line sloping down from left to right is a negative gradient The gradient using coordinates S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept Now try MIA Ex 4.2 Ch7 (page 143) www.mathsrevision.com The gradient using coordinates S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 1.To draw graphs by using a coordinate table 1.Understand the keypoints of drawing a straight line graph 2.Be able to plot a straight line graph Straight Line Graphs S4 Credit

11-May-15Created by Mr. Lafferty Maths Dept 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 y = x y = 2x y = 3x+1 y = x - 3 xyxy 0 0 3 3 -4 xyxy 0 0 3 6 -8 xyxy -2 -5 0 1 2 7 xyxy 0 -3 4 1 8 5 Drawing Straight Line Graphs y = ax + b

11-May-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Key Points 1.Make a table 2.Calculate and plot 3 coordinates 3. Draw a line through points Straight Line Graphs S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept Now try MIA Ex5.1 Q5 Only Ch7 (page 145) www.mathsrevision.com Straight Line Graphs S4 Credit

Q1.Write out in full to 2 sig. figs. 11-May-15Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com Q2.A superstore make 20% profit on each can of soup they sell. If they buy in a can for 50p. What is the selling price. Q3. Explain why 4x 2 – 16 = 4(x + 2)( x – 2) S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 2.Identity the gradient m from the standard form. 1.To explain the connection between the straight line equation and the gradient. 1.Understand the term standard form. The Straight Line Equation S4 Credit

11-May-15Created by Mr. Lafferty Maths Dept 0 1234567 8 910 -9-8 -7 -6 -5 -4-3-2 -10 x y 1 2 3 4 5 6 7 8 9 10 -2 -3 -4 -5 -6 -7 -8 -9 -10 y = 2x + 1 y = -x - 5 xyxy 0 1 1 3 3 7 xyxy 0 -5 1 -6 3 -8 Straight line equation and the gradient connection m = -1m = 2

11-May-15Created by Mr.Lafferty Maths Dept All straight lines have the equation of the form y = mx + c www.mathsrevision.com Straight Line Equation S4 Credit Let’s investigate properties (You need GeoGebra to run link)

11-May-15Created by Mr.Lafferty Maths Dept 74123568 10 0 1 2 3 4 5 6 7 8 9 9 x All straight lines have the equation of the form y = mx + c Gradient Where line meets y-axis y www.mathsrevision.com Straight Line Equation Find the equations of the following lines y = xy = x+4 lines are parallel if they have the same gradient y = 4x+2 y = -0.5x+2 S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept Now try MIA Ex 6.1 Ch7 (page 146) www.mathsrevision.com The Gradient of a Line S4 Credit

Q1.Write out in full to 1 significant fig. 11-May-15Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com Q2.A computer store buys in a laptop for £500. They want to make a 40% profit. How much do they sell it for. Q3. A line is parallel to y = 2x. Write down its equation S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept All straight lines have the equation of the form y = mx + c Gradient y - intercept www.mathsrevision.com Straight Line Equation y intercept is were line cuts y axis Slope left to right upwards positive gradient Slope left to right downwards negative gradient S4 Credit lines are parallel if same gradient

11-May-15www.mathsrevision.com Equation of a Straight Line To find the equation of a straight line we need to know Two points that lie on the line ( x 1, y 1 ) and ( x 2, y 2 ) Or The gradient and a point on the line m and (a,b) y = mx+c www.mathsrevision.com S4 Credit

Find the equation of the straight line passing through the points (4, 4) and (8,24). Solution y = mx+c www.mathsrevision.com S4 Credit Equation of a Straight Line Using the point (4,4) and the gradient m = 5 sub into straight line equation 4 = 5 x 4 + cc = 4 - 20 = -16 Equation : y = 5x - 16 y = mx + c 

Find the equation of the straight line passing through the points (3, -5) and (6,4). Solution y = mx+c www.mathsrevision.com S4 Credit Equation of a Straight Line Using the point (6,4) and the gradient m = 3 sub into straight line equation 4 = 3 x 6 + cc = 4 - 18 = -14 Equation : y = 3x - 14 y = mx + c 

11-May-15Created by Mr.Lafferty Maths Dept Now try MIA Ex 6.2 Ch7 (page 147 ) www.mathsrevision.com Straight Line Graphs S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com Q1.The points ( 1, 4) and (3, 11) lie on a line. Find the gradient of the line. Q2. Complete the table given :y = 3x + 1 Q3.Are the two lines parallel. Explain your answer y = x + 2 and y = 2x + 2 x-303 y S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 1.How to model real life situations using straight line theory 1.Be able to work out gradient and y intercept using a graph. Modelling Using Straight Line Equation 2.Form an equation for any straight line graph. S4 Credit

Modelling Real – life The cost for hiring a plumber per hour is shown below (a)Calculate the gradient. (b)What is the value of C when T = 0 (c)Write down an equation connecting C and T. Pick any 2 points (7,100) (0,30) 30 C = 30 T+ 10 (d)Find the cost for a plumber for 10 hours? T = 10C = 10 x 10 + 30 = £130

80 -5 Modelling Real – life The graph shows how a the volume of water tank drains over time. (a)Calculate the gradient. (b)What is the value of V when T = 0 (c)Write down an equation connecting V and T. Pick any 2 points (8,40) (0,80) 80 V =T+ (d)How long before the tank is empty? V = 00 = -5 x T + 80T = (-80) ÷(–5) = 16mins

11-May-15Created by Mr.Lafferty Maths Dept Now try Ex 7.1 MIA (page 149) www.mathsrevision.com Straight Line Equation S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept Starter Questions www.mathsrevision.com Q1.The points ( 5, 7) and (7, 21) lie on the same line. Find the gradient of the line. Q2. Complete the table given :y = 2x + 10 Q3.Are the two lines parallel. Explain answer y = -2x + 1 and y = 2x + 1 x-303 y S4 Credit

11-May-15Created by Mr.Lafferty Maths Dept www.mathsrevision.com Learning Intention Success Criteria 1.How to model real life situations using straight line theory 1.Be able to work out gradient and y intercept using a graph. Best Fit Straight Line Equation 2.Form an equation for any straight line graph. S4 Credit

x c = 0 (b)Draw in the best-fit line and find an equation relating height and weight. 2.57 0 Best-Fitting Straight line Data was collected on pupils weight and height. Data is plotted below. (a)Is there correlation between height and weight. Pick any 2 points (70,180) h =w+ (d)What height is a pupils who weights 40 kgs? w = 40h = 2.57 x 40 = 102.8 cms x (0,0) Yes, a positive correlation

c = 1818 -1.25 (b)Draw in the best-fit line and find an equation relating value and year. Best-Fitting Straight line A survey was carried out on the value of cars depending on their age The data is plotted below. (a)Is there correlation between value and age. Pick any 2 points (8,8) v =y+ (d)What is the cost of a car after 4years? y = 4v = -1.25 x 4 + 18 = 13 x (0,18) Yes, a negative correlation x Value = £13 000

11-May-15Created by Mr.Lafferty Maths Dept Now try Ex 8.1 MIA (page 151) www.mathsrevision.com S4 Credit Best Fit Straight Line Equation

Example The graph shows an electrician’s charging system. He has a call-out charge plus an hourly rate. a) Work out the equation of the line. b) Calculate the cost of a 10 hour job. www.mathsrevision.com S4 Credit Exam Type Straight Line Questions

Exam Type Straight Line Questions a) Pick two convenient points on the line, say (0, 30) and (5, 80). Thinking of the form y = mx + c The y-intercept gives c = 30 = 10 The equation is: y = 10x + 30 The label on the y-axis is C and the label on the x-axis is T So the equation is C = 10 T + 30 So the equation is C = 10 T + 30 b) Find C when T = 10 C = 10 x 10 + 30 = 130 The cost of a 10 hr job is £130. www.mathsrevision.com S4 Credit

1. The tank of a car contains 5 litres of petrol. The graph below shows how the volume of petrol in this tank changes as a further 45 litres of petrol is pumped in at a steady rate for 60 seconds. Find the equation of the straight line in terms of V and t. www.mathsrevision.com S4 Credit Exam Type Straight Line Questions

In the diagram below. A is the point (-1, -7) and B is the point (4, 3). 2. (a) Find the gradient of the line AB. (b) AB cuts the y-axis at the point (0, -5). Write down the equation of the line AB. (c) The point (3k, k) lies on the line AB. Find the value of k. S4 Credit Exam Type Straight Line Questions

A water pipe runs between two buildings. These are represented by the points A and B in the diagram below. 3. (a) Using the information in the diagram, show that the equation of the line AB is 3y – x = 6. www.mathsrevision.com S4 Credit Exam Type Straight Line Questions

(b)An emergency outlet pipe has to be built across the main pipe. The line representing this outlet pipe has equation 4y + 5x = 46. Calculate the coordinates of the point on the diagram at which the outlet pipe will cut across the main water pipe. www.mathsrevision.com S4 Credit Exam Type Straight Line Questions

www.mathsrevision.com S4 Credit Exam Type Straight Line Questions

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