Graphing Linear Equations By Using Intercepts Before we

Graphing Linear Equations By Using Intercepts

Before we begin graphing, let’s review writing equations in standard form, ax + by = c. Example 1: Rewrite the equations in standard form. a) 3 x + 4 = 2 y b) 5 x – 2 y = 15 3 x – 2 y = – 4 c) 5 y – 4 x = 20 – 4 x + 5 y = 20 5(x – 3) = 2 y d) ½x + ¾y = 1 2 x + 3 y = 4

Linear Equation An equation for which the graph is a line

Solution Any ordered pair of numbers that makes a linear equation true.

X-intercept Where the line crosses the x -axis

X-intercept The x-intercept has a y coordinate of ZERO

X-intercept To find the xintercept, plug in ZERO for y and solve

Y-intercept Where the line crosses the y -axis

Y-intercept The y-intercept has an x-coordinate of ZERO

Y-intercept To find the yintercept, plug in ZERO for x and solve

1. Find your x-intercept: Let y = 0 -2 x + 3 y = 12 -2 x + 3(0) = 12 -2 x = 12 -2 -2 x = -6; (-6, 0) 2. Find your y-intercept: Let x = 0 -2(0) + 3 y = 12 3 3 y = 4; (0, 4) Graph -2 x + 3 y = 12 3. Graph both points and draw a line through them.

4 x + y = 8 1. Find your x-intercept: Let y = 0 4 x + 0 = 8 4 x = 8 4 4 x = 2; (2, 0) 2. Find your y-intercept: Let x = 0 0+y=8 y = 8; (0, 8) Graph 4 x – 8 = –y 3. Graph both points and draw a line through them.

-2 x + 3 y = 15 1. Find your x-intercept: Let y = 0 -2 x + 3(0) = 15 -2 x = 15 -2 -2 x = -15/2; (-15/2, 0) 2. Find your y-intercept: Let x = 0 -2(0) + 3 y = 15 3 3 y = 5; (0, 5) Graph 3 y – 15 = 2 x 3. Graph both points and draw a line through them.

2 x + 5 y = 10 1. Find your x-intercept: Hide the variable y Graph 2 x – 10 = – 5 y 2 x = 10 2 2 x = 5; (5, 0) 2. Find your y-intercept: Hide the variable x 5 y = 10 5 5 y=2 y = 2; (0, 2) 3. Graph both points and draw a line through them.

– 2 x – 5 y = 20 1. Find your x-intercept: Hide the variable y Graph – 5 y = 2 x + 20 -2 x = 20 -2 -2 x = -10; (-10, 0) 2. Find your y-intercept: Hide the variable x -5 y = 20 -5 -5 y = -4; (0, -4) 3. Graph both points and draw a line through them.

Determine the x- and y-int. of the ff. x-int. y-int. 1. 3 x + y = 3 2. 2 x + 5 y = 10 3. 4 x – 6 y = 12 4. 6 x = 2 y – 4 5. x = 2 y + 7 1 ___ 5 ___ 3 ___ -2/3 ___ 7 ___ 3 ___ 2 ___ -2 ___ -7/2 ___

Seatwork: A. Determine the x- and y-int. of the ff. x-int. 1. 2 x + y = 4 ___ 2. x – y = 5 ___ 3. y = –x + 3 ___ 4. y = 2 x + 3 ___ 5. x = y – 6 ___ B. Graph nos. 4 and 5 y-int. ___ ___ ___