CHAPTER 8 Intercepts and Slope-Intercept Form

Objectives The student will be able to: find the x- and y-intercepts of linear equations Write Standard for of Linear equation to Slope-Intercept equation (function form)

What does it mean to INTERCEPT a pass in football? The path of the defender crosses the path of the thrown football. In algebra, what are x- and y-intercepts?

What are the x- and y-intercepts? The x-intercept is where the graph crosses the x-axis. The y-coordinate is always 0. The y-intercept is where the graph crosses the y-axis. The x-coordinate is always 0. (2, 0) (0, 6)

Find the x- and y-intercepts. 1. x - 2y = 12 x-intercept: Plug in 0 for y. x - 2(0) = 12 x = 12; (12, 0) y-intercept: Plug in 0 for x. 0 - 2y = 12 y = -6; (0, -6)

Find the x- and y-intercepts. 2. -3x + 5y = 9 x-intercept: Plug in 0 for y. -3x - 5(0) = 9 -3x = 9 x = -3; (-3, 0) y-intercept: Plug in 0 for x. -3(0) + 5y = 9 5y = 9 y = ; (0, )

Find the x- and y-intercepts. 3. y = 7 ***Special case*** x-intercept: Plug in 0 for y. Does 0 = 7? No! There is no x-intercept. None What type of lines have no x-intercept? Horizontal! Remember VUXHOY? Horizontal lines…y = 7…y-int = (0, 7)

What is the x-intercept of 3x – 4y = 24? (3, 0) (8, 0) (0, -4) (0, -6) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

What is the y-intercept of -x + 2y = 8? (-1, 0) (-8, 0) (0, 2) (0, 4) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

What is the y-intercept of x = 3? (3, 0) (-3, 0) (0, 3) None 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Next Lesson: Converting Standard Form Linear Equation to Slope-Intercept Form Linear Equation

Important!!! This is a big concept in Algebra 1. You need to thoroughly understand this! Slope – Intercept Form y = mx + b m represents the slope b represents the y-intercept

Writing Equations When asked to write an equation, you need to know two things – slope (m) and y-intercept (b).

Example 1: Writing Equations Write an equation in slope-intercept form of the line that has a slope of 2 and a y-intercept of 6. To write an equation, you need two things: slope (m) = y – intercept (b) = We have both!! Plug them into slope-intercept form y = mx + b y = 2x + 6 2 6

Writing Equations Write an equation in slope-intercept form for the following: 1. 3. 2. 4.

y = -3x – 4 y = -4x – 3 y = -3x + 4 y = -4x + 3 Write the equation of a line that has a y-intercept of -3 and a slope of -4. y = -3x – 4 y = -4x – 3 y = -3x + 4 y = -4x + 3

To find the slope and y-intercept of an equation, write the equation in slope-intercept form: y = mx + b. Find the slope and y-intercept. y = 3x – 7 y = mx + b m = 3, b = -7

Find the slope and y-intercept. 2) y = x y = mx + b y = x + 0 3) y = 5 y = 0x + 5 m = b = 0 m = 0 b = 5

Find the slope and y-intercept. 5x - 3y = 6   m = b = -2

Find the slope and y-intercept. 2x + 2y = 4 Write it in slope-intercept form. (y = mx + b) 2x + 2y = 4 - 2x -2x 2y = -2x+4 2 2 2 y = -x + 2 m = -1 b = 2

Find the slope and y-intercept. x + 2y = 6 Write it in slope-intercept form. (y = mx + b) x + 2y = 6 - x - x 2y = -x + 6 2 2 2 y = - 1 x + 3 2 m = - 1 2 b = 3

Find the slope and y-intercept. 8x + 2y = -4 Write it in slope-intercept form. (y = mx + b) 8x + 2y = -4 -8x - 8x 2y = -8x - 4 2 2 2 y = - 4x - 2 m = -4 b = -2

Find the slope and y-intercept of y = -2x + 4 m = 2; b = 4 m = 4; b = 2 m = -2; b = 4 m = 4; b = -2