Question

Consider this system of equations. Which equation represents the first equation written in slope-intercept form?

5 x minus 2 y = 10. y = one-fourth x + 1.
y = five-halves x minus 5
y = five-halves x + 10
y = negative five-halves x + 10
y = negative 5 x minus 5

Answer 1

To convert the equation \( 5x - 2y = 10 \) into slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), follow these steps:

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

2. Isolate the term involving \( y \) by subtracting \( 5x \) from both sides:
\[
-2y = -5x + 10
\]

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

Now, we compare this result, \( y = \frac{5}{2}x - 5 \), to the given options:

- \( y = \frac{1}{4}x + 1 \)
- \( y = \frac{5}{2}x - 5 \)
- \( y = \frac{5}{2}x + 10 \)
- \( y = -\frac{5}{2}x + 10 \)
- \( y = -5x - 5 \)

The correct equation representing the first equation in slope-intercept form is:

\[
y = \frac{5}{2}x - 5
\]