Writing the Equation of a Line from a Graph

Two equations we can use… The slope-intercept form of a linear equation is y = mx + b. m represents the slope b represents the y-intercept We can use this equation when we can accurately read the y-intercept from the graph

Two equations we can use… The point-slope form of a linear equation is y – y1 = m(x – x1) m represents the slope (x1, y1) represents a point We can use this equation when we cannot accurately read the y-intercept from the graph

Example 1 y = mx + b b = -3 m = y = x - 3 x y +2 +3

Example 2 y = mx + b b = 1 m = y = x + 1 x y -2 +1

Example 3 y = mx + b b = 4 m = 0 y = 0x + 4, y = 4 x y

Example 4 x y There is no b m = undefined x = -3

Example 5 m = The y-intercept cannot be read off accurately If you are not sure about the y-intercept use this method Read any two points off m = x y (-2,4) (2,-3)

Example 5 continued Points (-2, 4) and (2, -3) Slope: m = Use slope and one point with y – y1 = m(x – x1) x y

Remember Parallel lines have the same slope and different y-intercepts. Perpendicular lines have slopes that are opposite reciprocals.

Homework Find the linear inequalities for each colored region in the provided design