# Created by Mr.Lafferty Maths Dept

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Created by Mr.Lafferty Maths Dept
Straight Line Graphs Int 2 Drawing Straight line graphs The gradient The gradient from coordinates The y intercept y = mx + c Other forms / rearranging equation 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
Starter Questions Int 2 Q1. A house is valued at £ Calculate its value after 4 years, if it appreciates by 5% each year. Q2. Calculate 3.36 x 70 to 2 significant figures. Q3. Calculate the volume of a cylinder with radius 5cm and height 100 cm. 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
Straight Line Graphs Int 2 Learning Intention Success Criteria To draw graphs by using a coordinate table Understand the key points of drawing a straight line graph Be able to plot a straight line graph 31-Mar-17 Created by Mr.Lafferty Maths Dept

Drawing Straight Line Graphs y = mx + c y = x
1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y x y 3 -4 y = 3x+1 3 -4 x y -2 2 -5 1 7 y = x - 3 y = 2x x y 4 8 x y 3 -4 -3 1 5 6 -8 31-Mar-17 Created by Mr. Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
Straight Line Graphs Int 2 Key Points Make a table Calculate and plot 3 coordinates 3. Draw a line through points 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
Straight Line Graphs Int 2 Now try Exercise 1 Odd numbers MIA (page 33) 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
Starter Questions Int 2 Q1. Write this number in full to 1 sig. figs Q2. Calculate the volume of the triangular prism. 20cm 12cm 8cm 31-Mar-17 Created by Mr.Lafferty Maths Dept

The Gradient of a Line www.mathsrevision.com Learning Intention
Success Criteria To explain how to calculate the gradient using right angled triangles Gradient is : change in vertical height divided by change in horizontal distance 2. Calculate simple gradients. 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
The Gradient Difference in y -coordinates Int 2 The gradient is the measure of steepness of a line Change in vertical height Change in horizontal distance Difference in x -coordinates The steeper a line the bigger the gradient 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
The Gradient Int 2 3 m = V = H 4 3 m = V = H 2 3 m = V = H 5 2 m = V = H 6 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
The Gradient Int 2 Round the class Exercise 2 MIA (page 36) 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
The Gradient of a Line Int 2 Learning Intention Success Criteria To explain positive and negative gradients using coordinates. Know gradient formula. 2. Calculate gradients given two coordinates. 31-Mar-17 Created by Mr.Lafferty Maths Dept

Mr. Lafferty The gradient using coordinates Int 2 m = gradient y-axis m = Y2 – Y1 X2 – X1 y2 We start by find the equation of a circle centre the origin. First draw set axises x,y and then label the origin O. Next we plot a point P say, which as coordinates x,y. Next draw a line from the origin O to the point P and label length of this line r. If we now rotate the point P through 360 degrees keep the Origin fixed we trace out a circle with radius r and centre O. Remembering Pythagoras’s Theorem from Standard grade a square plus b squared equal c squares we can now write down the equal of any circle with centre the origin. y1 O x-axis x1 x2 31-Mar-17

Mr. Lafferty The gradient using coordinates Int 2 Find the gradient of the line. m = gradient y-axis m = Y2 – Y1 X2 – X1 m = 10 – 4 5 – 2 We start by find the equation of a circle centre the origin. First draw set axises x,y and then label the origin O. Next we plot a point P say, which as coordinates x,y. Next draw a line from the origin O to the point P and label length of this line r. If we now rotate the point P through 360 degrees keep the Origin fixed we trace out a circle with radius r and centre O. Remembering Pythagoras’s Theorem from Standard grade a square plus b squared equal c squares we can now write down the equal of any circle with centre the origin. m = 6 = 2 3 O x-axis 31-Mar-17

Mr. Lafferty The gradient using coordinates Int 2 Find the gradient of the two lines. y-axis m = Y2 – Y1 X2 – X1 m = Y2 – Y1 X2 – X1 m = 3 - 1 m = 8 – 2 -3 – (-1) We start by find the equation of a circle centre the origin. First draw set axises x,y and then label the origin O. Next we plot a point P say, which as coordinates x,y. Next draw a line from the origin O to the point P and label length of this line r. If we now rotate the point P through 360 degrees keep the Origin fixed we trace out a circle with radius r and centre O. Remembering Pythagoras’s Theorem from Standard grade a square plus b squared equal c squares we can now write down the equal of any circle with centre the origin. m = 6 = -3 -2 m = 6 = 3 2 O x-axis 31-Mar-17

Int 2 The gradient formula is : Gradient = m = (y2 – y1) (x2 – x1) 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 31-Mar-17 Created by Mr.Lafferty Maths Dept

Int 2 Exercise 3 Q1 – Q3 MIA (page 37) 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
Starter Questions Int 2 Q1. Write out in full to 2 sig. figs. 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. A hemisphere has a diameter of 10cm. Calculate its volume. 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
The Gradient of a Line Int 2 Learning Intention Success Criteria To explain the connection between the straight line equation and the gradient. Understand the term standard form. 2. Identify the gradient m from the standard form. 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr. Lafferty Maths Dept
Straight line equation and the gradient connection 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y y = -x - 5 y = 2x + 1 x y 1 3 x y 1 3 -5 -6 -8 1 3 7 m = -1 m = 2 31-Mar-17 Created by Mr. Lafferty Maths Dept

Straight Line Equation
S4 Credit All straight lines have the equation of the form y = mx + c Let’s investigate properties (You need GeoGebra to run link) 31-Mar-17 Created by Mr.Lafferty Maths Dept

Straight Line Equation
y 10 lines are parallel if they have the same gradient All straight lines have the equation of the form 9 8 y = mx + c 7 6 5 4 3 Where line meets y-axis 2 Gradient 1 x 1 2 3 4 5 6 7 8 9 10 Find the equations of the following lines y = x y = x+4 y = 4x+2 y = -0.5x+2 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
The Gradient of a Line Int 2 Now try Exercise 3 Q4 – Q9 MIA (page 38) 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
Starter Questions Int 2 Q1. Write out in full to 1 significant fig. 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 31-Mar-17 Created by Mr.Lafferty Maths Dept

Straight Line Equation
lines are parallel if same gradient Straight Line Equation All straight lines have the equation of the form Slope left to right upwards positive gradient y = mx + c y - intercept Gradient y intercept is were line cuts y axis Slope left to right downwards negative gradient 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
Straight Line Graphs Int 2 Now try Exercise 4 MIA (page 41 ) 31-Mar-17 Created by Mr.Lafferty Maths Dept

Created by Mr.Lafferty Maths Dept
Starter Questions Int 2 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 x -3 3 y Q3. Are the two lines parallel. Explain answer y = x and y = 2x + 2 31-Mar-17 Created by Mr.Lafferty Maths Dept

Straight Line Equation
Int 2 Learning Intention Success Criteria To show how to rearrange straight line equations into standard form and then identify the gradient and the y - intercept. Be able to rearrange straight line equations. y = mx + c Identify the gradient m and y – intercept c from the standard form. y = mx + c 31-Mar-17 Created by Mr.Lafferty Maths Dept

Straight Line Equation
This is called the standard form Straight Line Equation All straight lines have an equation of the form y = mx + c Where line meets y-axis Gradient If two lines have the same gradient they are parallel. y = 2x y = 2x+4 31-Mar-17 Created by Mr.Lafferty Maths Dept

Straight Line Equation
Just a bit of algebra Straight Line Equation Rearrange the following straight line equations into standard form and identify the gradient and y-intercept. Standard form m c y – 3x = 4 y = 3x + 4 3 4 2y – 2x = 6 y = x + 3 1 3 y – x + 5 = 0 y = x - 5 1 -5 4y – 8 = 0 y = 2 2 31-Mar-17 Created by Mr.Lafferty Maths Dept

Straight Line Equation
Find the a line parallel to y – x = 0 and passing through (0,3). Standard form m c x – y = 0 y = x 1 A line parallel to y = x has same gradient therefore m = 1 Since it passes through (0,3) then c = 3 Using standard form line is y = x + 3 31-Mar-17 Created by Mr.Lafferty Maths Dept

Straight Line Equation
Int 2 Now try Ex 5 MIA (page 45) 31-Mar-17 Created by Mr.Lafferty Maths Dept