Objective The student will be able to: find the x- and y-intercepts of linear equations.

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)

List the points along the x axis, what do you notice? … (-5,0) (-4,0) (-3,0) (-2,0) (-1,0) (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) All y values are 0

List the points along the y axis, what do you notice? … (0,-5) (0,-4) (0,-3) (0,-2) (0,-1) (0,0) (0,1) (0,2) (0,3) (0,4) (0,5) All x values are 0

Intercepts: Find the x and y intercepts then graph the line y intercept x=0 Substitute o in for x then solve for y X intercept y=0 Substitute o in for y then solve for x

Graph of equation First graph the x intercept x=-5 at the point (-5,0) Then graph the y intercept y=-4 at the point (0,-4) Finally connect the points to form a line

Intercepts: Find the x and y intercepts then graph the line y intercept x=0 Substitute o in for x then solve for y X intercept y=0 Substitute o in for y then solve for x

Graph of equation First graph the x intercept x=12 at the point (12,0) (change scale count by twos. Then graph the y intercept y=-8 at the point (0,-8) Finally connect the points to form a line

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

Find the x- and y-intercepts of 2x + 3y = 6 using the graphing calculator. Before using the calculator, you must solve the equation for y first. 3y = -2x + 6 y = + 2 Type the equation in the Graph menu and graph it.

Your graph should look like this Your graph should look like this. It may vary depending on your window size. Press F5 (G-Solv) and select F1 (Root) to determine the x-intercept. The x-intercept is (3, 0)

Now find the y-intercept! Press F4 (Y-ICPT) for the y-intercept. y-intercept = (0, 2)