 # X and Y Intercepts. Definitions Intercept – the point where something intersects or touches.

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X and Y Intercepts

Definitions Intercept – the point where something intersects or touches

X -intercept – where the line touches the x-axis x-intercept The x-intercept always has a y of “0” (3, 0) Definitions

Y -intercept – where the line touches the y-axis y-intercept The y-intercept always has a x of “0” (0, 4) Definitions

Identify the Intercepts X- intercept: Y - intercept: (-4, 0) (0, 2)

Identify the Intercepts X- intercept: Y - intercept: (5, 0) (0, -7)

Intercepts to Graph Equations We know that for the x-intercept, the y-coordinate is always 0 (zero) and that for the y-intercept, the x-coordinate is always 0 (zero) We can use this information to solve equations and to graph a line.

To solve for the “Y” intercept – plug in 0 (zero) for x Intercepts to Graph Equations To solve for the “X” intercept – plug in 0 (zero) for y This is similar to picking a number for x (-1, 0, 1, 2, etc), plugging it in and solving for y. The only difference is that in this situation I want specific points – the intercepts.

Intercepts to Graph Equations Step 1: Find the Intercepts 2x + 3y = 6 Find the y-intercept 2x + 3y = 6 2(0) + 3y = 6 3y = 6 3 = 3 y = 2 y – intercept = (0, 2) Find the x-intercept 2x + 3y = 6 2x + 3(0) = 6 2x = 6 2 = 2 x = 3 x – intercept = (3, 0)

Intercepts to Graph Equations Step 2: Use the intercepts to graph the line 2x + 3y = 6 y – intercept = (0, 2) x – intercept = (3, 0)

Intercepts to Graph Equations Step 1: Find the Intercepts 6x - 4y = 24 Find the y-intercept 6x - 4y = 24 6(0) - 4y = 24 -4y = 24 -4 = -4 y = -6 y – intercept = (0, -6) Find the x-intercept 6x - 4y = 24 6x - 4(0) = 24 6x = 24 6 = 6 x = 4 x – intercept = (4, 0)

6x - 4y = 24 Intercepts to Graph Equations Step 2: Use the intercepts to graph the line y – intercept = (0, -6) x – intercept = (4, 0)

Intercepts to Graph Equations Step 1: Find the Intercepts y - 3x = 9 Find the y-intercept y - 3x = 9 y - 3(0) = 9 y = 9 y – intercept = (0, 9) Find the x-intercept y - 3x = 9 0 - 3x = 9 -3x = 9 -3 = -3 x = -3 x – intercept = (-3, 0)

Intercepts to Graph Equations Step 2: Use the intercepts to graph the line y – intercept = (0, 9) x – intercept = (-3, 0) y - 3x = 9

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