Using a Point & Slope to find the Equation

What we are doing today…. We are going to learn how to take a point and a slope and turn it into y = mx + b. For example: (3, 5) and m = 2 will become y = 2x - 1

Finding an equation When given a point and a slope – For example, find the equation of a line with the point (2, 8) and a slope of 3 First, use the slope-intercept equation y=mx+b Look at the information you are given (2, 8) and a slope of 3 Plug these into y = mx + b Our new problem looks like 8= 3(2) + b Let’s simplify 8 = 6 + b -6 2 = b x y m

We now know the slope and y-intercept m = 3 b = (0, 2) Let’s plug into y = mx + b y = 3x + 2

Finding an equation When given a point and a slope – For example, find the equation of a line with the point (-2, 3) and a slope of -4 First, use the slope-intercept equation y=mx+b Look at the information you are given (-2, 3) and a slope of -4 Plug these into y = mx + b Our new problem looks like 3= -4(-2) + b Let’s simplify 3 = 8 + b = b x y m

We now know the slope and y-intercept m = -5 b = (0, -4) Let’s plug into y = mx + b y = -5x – 4

Finding an equation When given a point and a slope – For example, find the equation of a line with the point (-8, -6) and a slope of 1/2 First, use the slope-intercept equation y=mx+b Look at the information you are given (-8, -6) and a slope of 1/2 Plug these into y = mx + b Our new problem looks like -6= 1/2(-8) + b Let’s simplify -6 = -4 + b = b x y m

We now know the slope and y-intercept m = 1/2 b = (0, -2) Let’s plug into y = mx + b y = 1/2x – 2

Finding an equation You try these problems A)(1, 8) m = 4 B)(-3, -5) m = 1/3 C)(0, 5) m = -2 D)(6, 2) m = 0 y = 4x + 4 y = x – 2 y = -2x + 5 y = 2

Practice Write a linear equation using the point and the slope for the following. Then graph the line. 1.(1,1) and m =1/42. (6,0) and m = -1/2 3.(-2,1) and m = 14. (-6,-2) and m = -1/3 5. (3,-4) and m = 06. (-4,1) and m = 3/2 7. (0,0) and m = -38. (5,-3) and m = none/ undefined