Question

Select the equation that is parallel to y=(1/2)x-3 and goes through (-6,-8)

a
y=(1/2)x+5

b
y=(1/2)x-5

c
y=-2x+7

d
y=-2x-3

Answer 1

To find the equation of a line that is parallel to \( y = \frac{1}{2}x - 3 \) and goes through the point \((-6, -8)\), we need to:

1. Use the same slope as the given line. The slope of \( y = \frac{1}{2}x - 3 \) is \(\frac{1}{2}\).
2. Use the point-slope form of the equation to find the equation of the line that passes through the point \((-6, -8)\).

The point-slope form of the equation is:

\[
y - y_1 = m(x - x_1)
\]

where \( m \) is the slope and \( (x_1, y_1) \) is the point.

Substituting the values:

\[
y - (-8) = \frac{1}{2}(x - (-6))
\]

This simplifies to:

\[
y + 8 = \frac{1}{2}(x + 6)
\]

Now, distribute \(\frac{1}{2}\):

\[
y + 8 = \frac{1}{2}x + 3
\]

Next, isolate \( y \):

\[
y = \frac{1}{2}x + 3 - 8
\]

\[
y = \frac{1}{2}x - 5
\]

Now we can compare this result to the options provided.

The correct equation is:

**b) \( y = \frac{1}{2}x - 5 \)**.