Question

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

One-half (2 y + 10) = 7 x. y = 8.
y = 7 x minus 10
y = StartFraction 7 Over 2 EndFraction x minus 5
y = 7 x minus 5
y = StartFraction 7 Over 4 EndFraction x minus 5

Answer 1

To convert the equation \(\frac{1}{2}(2y + 10) = 7x\) into slope-intercept form (which is \(y = mx + b\)), we can start by simplifying the given equation.

1. Distribute \(\frac{1}{2}\) on the left side:
\[
\frac{1}{2}(2y) + \frac{1}{2}(10) = 7x
\]
This simplifies to:
\[
y + 5 = 7x
\]

2. To solve for \(y\), we subtract 5 from both sides:
\[
y = 7x - 5
\]

Now we have the equation in slope-intercept form, where \(m = 7\) and \(b = -5\).

Therefore, the correct answer is:
\[
y = 7x - 5
\]