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15-Feb-14Created by Mr.Lafferty Maths Dept www.mathsrevision.com The Gradient Change in vertical height Change in horizontal distance The gradient is the.

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Presentation on theme: "15-Feb-14Created by Mr.Lafferty Maths Dept www.mathsrevision.com The Gradient Change in vertical height Change in horizontal distance The gradient is the."— Presentation transcript:

1 15-Feb-14Created by Mr.Lafferty Maths Dept 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

2 15-Feb-14Created by Mr.Lafferty Maths Dept The Gradient S4 Credit

3 m = gradient x1x1 15-Feb-14www.mathsrevision.com 3 y-axis O x-axis The gradient using coordinates x2x2 y2y2 y1y1 S4 Credit

4 m = gradient 15-Feb-14www.mathsrevision.com 4 y-axis O x-axis The gradient using coordinates Find the gradient of the line. S4 Credit

5 15-Feb-14www.mathsrevision.com 5 y-axis O x-axis The gradient using coordinates Find the gradient of the two lines. S4 Credit

6 15-Feb-14Created by Mr.Lafferty Maths Dept 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

7 15-Feb-14Created by Mr.Lafferty Maths Dept Key Points 1.Make a table 2.Calculate and plot 3 coordinates 3. Draw a line through points Straight Line Graphs S4 Credit

8 15-Feb-14Created by Mr. Lafferty Maths Dept x y y = x y = 2x y = 3x+1 y = x - 3 xyxy xyxy xyxy xyxy Drawing Straight Line Graphs y = ax + b

9 15-Feb-14Created by Mr. Lafferty Maths Dept x y y = 2x + 1 y = 2x - 5 xyxy xyxy Straight line equation and the gradient connection m = 2

10 15-Feb-14Created by Mr.Lafferty Maths Dept x All straight lines have the equation of the form y = mx + c Gradient Where line meets y-axis y 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 x y Feb-14Created 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

12 15-Feb-14Created by Mr.Lafferty Maths Dept All straight lines have the equation of the form y = mx + c Gradient y - intercept 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

13 15-Feb-14www.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 S4 Credit

14 Find the equation of the straight line passing through the points (4, 4) and (8,24). Solution y = mx+c 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 = = -16 Equation : y = 5x - 16 y = mx + c

15 Find the equation of the straight line passing through the points (3, -5) and (6,4). Solution y = mx+c 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 = = -14 Equation : y = 3x - 14 y = mx + c

16 15-Feb-14Created by Mr.Lafferty Maths Dept Starter Questions 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

17 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 = £130


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