Question

Rewrite the equation in slope intercept form, identify the slope and y-intercept, and select the correct graph.

2x - 5y = 10

Answer 1

To rewrite the equation \(2x - 5y = 10\) in slope-intercept form (\(y = mx + b\)), we need to solve for \(y\).

1. Start with the original equation:
\[
2x - 5y = 10
\]

2. Subtract \(2x\) from both sides:
\[
-5y = -2x + 10
\]

3. Divide each term by \(-5\):
\[
y = \frac{2}{5}x - 2
\]

Now, the equation is in the slope-intercept form \(y = mx + b\), where:
- \(m\) (the slope) is \(\frac{2}{5}\)
- \(b\) (the y-intercept) is \(-2\)

So, the slope is \(\frac{2}{5}\) and the y-intercept is \(-2\).

To select the correct graph, look for:
1. A line with a slope that rises \(2\) units for every \(5\) units it moves to the right.
2. The line crossing the y-axis at \(-2\).

This information should help you identify the correct graph corresponding to the equation.