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Understanding X and Y Intercepts in Graphing Linear Equations

In this lesson, we will explore how to find the x and y intercepts of linear equations in the form Ax + By = C. The goal is to convert the equation to slope-intercept form, y = mx + b, by isolating the y variable. The y-intercept, denoted as "b," is where the line crosses the y-axis, while the x-intercept is where it crosses the x-axis. We will practice finding the intercepts for equations like 3x + 4y = 12 and 2x - y = 4, and complete homework exercises to reinforce these concepts.

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Understanding X and Y Intercepts in Graphing Linear Equations

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  1. Ax + By = C Form:x- and y- intercepts Lesson 5-7

  2. Review When given Ax + By = C, and asked to graph…  y = mx + b **goal: is to change to y = mx + b, by ISOLATING the y y-intercept (aka “b”): The point at which a line on a graph intercepts/crosses the y-axis x-intercept: The point at which a line on a graph intercepts/crosses the x-axis

  3. X- and Y- Intercepts X- and Y- intercepts… what does that mean? WHERE on the x-axis/y-axis the line passes (Just TWO points  on x and y)

  4. X- and Y- Intercepts Find the x- and y- intercepts of the equation: 3x + 4y= 12 Find the x-intercept: 3x + 4y = 12 *let y = 0 3x + 4(0) = 12 3x = 12 x = 4 Find the y-intercept: 3x + 4y = 12 *let x= 0 3(0) + 4y= 12 4y= 12 y= 3

  5. X- and Y- Intercepts Find the x- and y- intercepts of the equation: 2x – y = 4 Find the x-intercept: 2x – y = 4 *let y = 0 2x – (0) = 4 2x = 4 x = 2 Find the y-intercept: 2x – y= 4 *let x= 0 2(0) – y = 4 -y= 4 y= -4

  6. Practice Find the x- and y- intercepts of: A) 10x – 2y = 20 B) 5x + 2y = -10

  7. Homework p. 249 #15, 18, 19, 20, 22 (solve x- and y-) #33,34, 35-38 (graph all problems BUT 33, 34)

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