Math  /  Geometry

QuestionGraph the following. 3) y=23x2y=\frac{2}{3} x-2

Studdy Solution

STEP 1

1. The equation y=23x2 y = \frac{2}{3}x - 2 is a linear equation.
2. The graph of a linear equation is a straight line.

STEP 2

1. Identify the slope and y-intercept from the equation.
2. Plot the y-intercept on the graph.
3. Use the slope to find another point on the line.
4. Draw the line through the points.

STEP 3

Identify the slope and y-intercept from the equation y=23x2 y = \frac{2}{3}x - 2 .
- The slope m m is 23 \frac{2}{3} . - The y-intercept b b is 2-2.

STEP 4

Plot the y-intercept on the graph.
- The y-intercept is the point where the line crosses the y-axis. - Plot the point (0,2) (0, -2) on the graph.

STEP 5

Use the slope to find another point on the line.
- The slope 23 \frac{2}{3} means that for every 3 units you move to the right along the x-axis, you move 2 units up along the y-axis. - Starting from the y-intercept (0,2) (0, -2) , move 3 units to the right to x=3 x = 3 , and 2 units up to y=0 y = 0 . - Plot the point (3,0) (3, 0) .

STEP 6

Draw the line through the points.
- Draw a straight line through the points (0,2) (0, -2) and (3,0) (3, 0) . - Extend the line across the graph.
The graph of the equation y=23x2 y = \frac{2}{3}x - 2 is a straight line passing through the points (0,2) (0, -2) and (3,0) (3, 0) .

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