6 minutes Warm-Up 1. Find the slope of the line containing the points (-2,5) and (4,6). 2. Find the slope of the line y = x – 9. 3. Find the slope of the line 3y – 4x = 9.

Equation of a Line Objectives: To write an equation of a line using the slope-intercept equation To write an equation of a line using the point-slope equation

The Slope-Intercept Equation y = mx + b slope y-intercept Create an equation of a line with a slope of -3 and a y-intercept of 4. y = -3x + 4 y = 4 – 3x 3x = 4 - y -4 = -y – 3x

Example 1 y = mx + b 4 = 3 (-2) + b 4 = -6 + b +6 +6 10 = b Write an equation for the line with slope 3 that contains the point (-2,4) y = mx + b solve for b 4 = 3 (-2) + b substitute simplify 4 = -6 + b +6 +6 10 = b y = 3x + 10

Practice Write an equation for the given line that contains the given point and has the given slope. 1) (5,10); m = 4 2) (-3,8); m = 2

Example 2 Write an equation for the line containing the points (1,5) and (2,8).

Example 2 y = mx + b 5 = 3 (1) + b 5 = 3 + b -3 -3 2 = b y = 3x + 2 Write an equation for the line containing the points (1,5) and (2,8). y = mx + b substitute 5 = 3 (1) + b simplify 5 = 3 + b -3 -3 2 = b y = 3x + 2

Practice 1 Write an equation for the line that contains the given points. 1) (-4,1) (-1,4) 2) (-3,5) (-1,-3)

Practice 2 1. Write an equation for the line with slope -2 and containing the point (-3,0). 2. Write an equation for the line containing the points (0,0) and (4,2).

The Point-Slope Equation y – y1 = m(x – x1) Create an equation of a line with a slope of -3 that contains the point (7,2). y – 2 = -3(x – 7) y – 2 = -3x + 21 +2 +2 y = -3x + 23

Example 1 Write an equation for the line with slope 7 that contains the point (3,4). y – y1 = m(x – x1) y – 4 = 7(x – 3) y – 4 = 7x - 21 +4 +4 y = 7x - 17

Practice Write an equation for the line with the given point and slope. 1) (-3,0), m = -3 2) (4,3), m = ¾

Example 2 Write an equation for the line containing (5,7) and (2,1). First, find the slope: y – y1 = m(x – x1) y – 7 = 2(x – 5) y – 7 = 2x - 10 +7 +7 y = 2x - 3

Practice Write an equation for a line containing the following points. 1) (12,16) (1,5) 2) (-3,5) (-1,-3)

Example 3 Write an equation for the line shown below. First, find any two points on the line. (-3,-3) and (1,-1) 4 2 -4 -2 2 4 y – y1 = m(x – x1) -2 -4 y + 3 = ½(x + 3) y + 3 = ½x + 1½ -3 -3 y = ½x – 1½