Question

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

y = 3 x minus 2. 10 (x + three-fifths) = 2 y
y = 5 x + StartFraction 3 Over 10 EndFraction
y = 5 x + 3
y = one-fifth x + StartFraction 3 Over 25 EndFraction
y = one-half x + 6

Answer 1

To convert the second equation \(10(x + \frac{3}{5}) = 2y\) into slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), we need to follow these steps:

1. Distribute the 10 on the left side:
\[
10x + 10 \cdot \frac{3}{5} = 2y
\]
Simplifying \(10 \cdot \frac{3}{5}\):
\[
10 \cdot \frac{3}{5} = 6
\]
So the equation becomes:
\[
10x + 6 = 2y
\]

2. Solve for \(y\) by dividing the entire equation by 2:
\[
y = \frac{10}{2}x + \frac{6}{2}
\]
Which simplifies to:
\[
y = 5x + 3
\]

Thus, the second equation written in slope-intercept form is:
\[
y = 5x + 3
\]

Among the options given, the correct one is:
- \(y = 5x + 3\)