OBJECTIVE I will use slope-intercept form to write an equation of a line.

Vocabulary Slope-intercept form - an equation of a line that uses the slope and y-intercept y = mx + b Slope-intercept form f(x) = mx + b Linear function m = slope b = y-intercept

Writing an Equation of a Line Write an equation of the line whose slope is -4 and y-intercept is 6. y = mx + b Write equation for slope- intercept form y = -4x + 6 Substitute

Guided Practice Write an equation of the line whose slope is 3 and y-intercept is -8.

Writing an Equation of a Line from a Graph y = mx + b Equation y = 3x + (-2) Substitute y = 3x - 2 Simplify (0, -2), (1, 1)

Guided Practice

Writing an Equation of a Line Given its Slope and a Point Step 1: Find the y-intercept. Substitute all known variables (coordinates of the point (x, y) and slope m) and substitute into the equation for slope-intercept form (y = mx + b) Solve for the y-intercept b Step 2: Write the equation of the line. Substitute the slope m and y-intercept b into the slope-intercept form, y = mx + b. 7

Writing an Equation of a Line Write an equation of the line that passes through the point (-4, 2) and has a slope of 2. Step 1: Find the y-intercept. y = mx + b Slope-intercept form 2 = 2(-4) + b Substitute 2 = -8 + b Multiply 10 = b Add 8 to both sides 8

Writing an Equation of a Line Write an equation of the line that passes through the point (-4, 2) and has a slope of 2. Step 2: Write the equation of the line. y = mx + b Slope-intercept form y = 2x + 10 Substitute 2 for m and 14 for b Check Graph 9

Guided Practice Write an equation of the line that passes through the point (3, -2) and has a slope of -3. 10

Writing an Equation of Parallel Lines Write an equation of the line that is parallel to the line y = 3x + 1 and passes through the point (1, 1). Parallel Lines: m1 = m2 3 = m2 y = mx + b Slope-intercept form 1 = 3(1) + b Substitute for coordinates and slope 1 = 3 + b Multiply -2 = b Subtract 3 from both sides 11

Writing an Equation of Parallel Lines Write an equation of the line that is parallel to the line y = 3x + 1 and passes through the point (1, 1). y = mx + b Slope-intercept form y = 3x + (-2) Substitute 3 for m and -2 for b y = 3x - 2 Simplify Check Graph 12

Guided Practice Write an equation of the line that is parallel to the line y = (1/2)x - 2 and passes through the point (-1, 2). 13

Writing an Equation of a Line Given Two Points Step 1: Find the slope. Substitute the coordinates of the two points into the formula for slope, Step 2: Find the y-intercept. Substitute the slope m and the coordinates of one of the points into slope-intercept form, y = mx + b, and solve for the y-intercept b. Step 3: Write the equation of the line. Substitute the slope m and y-intercept b into the slope-intercept form, y = mx + b. 14

Writing an Equation of a Line Given Two Points Write an equation of the line that passes through the points (-3, 2) and (2, 7). Step 1: Find the slope. Formula for slope Substitute Add/Subtract Divide/Simplify 15

Writing an Equation of a Line Given Two Points Write an equation of the line that passes through the point (-3, 2) and (2, 7). Step 2: Find the y-intercept. y = mx + b Slope-intercept form 7 = 1(2) + b Substitute 7 = 2 + b Multiply 5 = b Subtract 2 from both sides 16

Writing an Equation of a Line Given Two Points Write an equation of the line that passes through the point (-3, 2) and (2, 7). Step 3: Write an equation of the line. y = mx + b Slope-intercept form y = 1x + 5 Substitute y = x + 5 Simplify 17

Guided Practice Write an equation of the line that passes through the point (6, 1) and (-2, 8). 18

Writing an Equation of Perpendicular Lines Write an equation of the line that is perpendicular to the line that passes through the points (1, 1) and (5, 9). Find the slope of the first line: Find slope of second line. Perpendicular Lines: m1 • m2 = -1 (Negative Reciprocals) 2 • m2 = -1 m2 = -1/2 19

Writing an Equation of Perpendicular Lines Write an equation of the line that is perpendicular to the line that passes through the points (1, 1) and (5, 9). y = mx + b Slope-intercept form 1 = (-1/2)(1) + b Substitute 1 = (-1/2) + b Multiply 3/2 = b Add 1/2 to both sides y = mx + b Re-write original equation y = (-1/2)x + 3/2 Substitute for m and b 20

Guided Practice Write an equation of the line that is perpendicular to the line that passes through the point (-1, 2) and (4, 3). 21

Independent Practice Write an equation of a line with a slope of -7 and a y-intercept of -2. Write an equation of the line on the graph. Use the equation to find y when x = 10.

Independent Practice Write an equation of the line that passes through the point (-2, -3) and has a slope of 5. Write an equation of the line the line that is parallel to the line y = -3x + 2 and passes through the point (1, -4). Between 2005 and 2008, the cost of an Xbox 360 decreased $100 per year. In 2006, the cost of an Xbox 360 was $399. Write a linear equation that relates the cost of the system y in terms of the year t. Let t be the number of years since 2005. Then find the cost of an Xbox 360 in 2008. 23

Independent Practice Write an equation of the line that passes through the points (-2, -3) and (2, 3). Write an equation of the line the line that is perpendicular to the line that passes through the points (-2, -3) and (2, 3). 24