20/11/2019 WALT: Grad. & Intercept Understand that linear functions in the form y=mx+c represent a straight line. WILF: Is the answer to: Is the answer to: Write down the gradient and y-intercept for the linear function Write down the gradient and y-intercept for the linear function y = 3x – 1 y = 3x – 1 Keywords Level 6 1 of 52 Gradient Level 6 Y-intercept Level 6 Is for youto: find the function of a straight line from a graph Level 7 y 8 y 2x 8 7 y 2x 4 y 2x 6 Here are 4 equations: y = 2x y = 2x + 8 y = 2x + 4 y = 2x – 6 The equations have been plotted on the graph to the left. 5 4 3 y 2x 6 2 Looking at all equations and all the corresponding graphs. Write down some observations you have made (what is similar/ what is different/ how do the graphs link to the equations). 1 -4 -3 -2 -1 -1 -2 -3 -4 -5 -6 -7 -8 2 of 52 1 2 3 4 x ........................................................... ........................................................... ........................................................... ........................................................... ........................................................... ........................................................... ........................................................... ........................................................... y 8 y 4x 1 y 2x 1 7 6 Here are 4 equations: y = 2x + 1 y = -x + 1 y = 4x + 1 y = ½x + 1 The equations have been plotted on the graph to the left. 5 4 3 y 2 Looking at all equations and all the corresponding graphs. Write down some observations you have made 1 x 1 (what is similar/ what is different/ how do the graphs link to the 2 equations). 1 -4 -3 -2 -1 -1 1 2 3 4 x -2 -3 -4 -5 -6 -7 -8 3 of 52 y x 1 ........................................................... ........................................................... ........................................................... ........................................................... ........................................................... ........................................................... ........................................................... ........................................................... 20/11/2019 Grad. & Intercept Definition The general equation of a straight line can be written as: y = mx + c The value of m tells us the gradient of the line. The value of c tells us where the line crosses the y-axis. This is called the y-intercept and it has the coordinate (0, c). For example, the line y = 3x + 4 has a gradient of 3 and crosses the yaxis at the point (0, 4). 4 of 52 20/11/2019 Gradient: Grad. & Intercept M stands for the gradient 5 5 4 4 3 3 2 2 1 1 0 0 0 1 2 3 4 5 m=1 5 of 52 5 4 3 2 1 0 0 1 2 3 4 5 0 1 2 3 4 5 m=3 m=½ Grad. & Intercept 20/11/2019 Y- Intercept: C stands for the Intercept -1 -2 -1 -2 1 2 3 c=2 6 of 52 3 2 1 3 2 1 3 2 1 -1 -2 -1 -2 1 2 3 c=0 -1 -2 -1 -2 1 2 3 c = -1 20/11/2019 Example: Grad. & Intercept Find the Gradient and y intercept of these linear functions. a) y =3x – 4 Gradient =2 Y-intercept =1 b) y = ½x + 5 Gradient =½ Y-intercept =5 7 of 52 20/11/2019 Grad. & Intercept Exercise 1: Complete this table: 8 of 52 equation gradient y = 3x + 4 3 4 x y= –5 2 1 2 –5 y = 2 – 3x –3 2 y=x 1 0 y = –2x – 7 –2 –7 y-intercept 20/11/2019 Example: Grad. & Intercept Find the Gradient and y intercept of these lines. 6 6 Gradient =2 4 -2 4 Y-intercept =1 2 2 4 6 -2 2 -2 -4 -4 9 of 52 Y-intercept =3 2 -2 y=2x + 1 Gradient = -3 4 y=-3x + 3 6 Grad. & Intercept 20/11/2019 Exercise 2: Name the function for each line. E B A C y 14 12 10 8 6 F 4 2 -8 -6 -4 -2 -2 -4 -6 10 of 52 2 4 6 8 x D a x=3 b y = 3x - 3 c y=x+4 d y = -2 e y = -2x + 9 f y = -½x - 1 20/11/2019 Example: Grad. & Intercept Draw these linear functions Gradient =2 6 4 Y-intercept =-2 2 -2 2 -2 -4 11 of 52 y=2x - 2 4 6 20/11/2019 Grad. & Intercept Exercise 3: Draw the following graphs without a table of values X-axis from -2 to 4 and the y-axis from -10 to 10 1 2 3 4 12 of 52 y = 2x 5 y = ½x - 9 y = 2x + 3 6 y = -x + 6 y = 4x -1 7 y = -2x y = 3x - 4 7 y = -3x - 2 20/11/2019 WALT: Grad. & Intercept Understand that linear functions in the form y=mx+c represent a straight line. WILF: Is the answer to: Is the answer to: Write down the gradient and y-intercept for the linear function Write down the gradient and y-intercept for the linear function y = 3x – 1 y = 3x – 1 Keywords Level 6 13 of 52 Gradient Level 6 Y-intercept Level 6 Is for youto: find the function of a straight line from a graph Level 7 y 8 y 2x 2 Here is the line y = 2x + 2 7 6 1) Move the line y = 2x + 2 two places to the right 5 4 2) Write the equation of the new line 3 ________________________ 2 1 -4 -3 -2 -1 -1 1 2 3 4 3) Move the line y = 2x + 2 three places to the left 4) Write the equation of the new line x -2 -3 -4 -5 -6 -7 -8 14 of 52 _________________________