Question

The equation for line g can be written as y–8=
–
2(x–4). Line h is parallel to line g and passes through (
–
5,1). What is the equation of line h?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Answer 1

First, we start with the equation of line \( g \):

\[
y - 8 = -2(x - 4)
\]

To put this into slope-intercept form (y = mx + b), we can simplify it:

1. Distribute \(-2\) on the right side:

\[
y - 8 = -2x + 8
\]

2. Add \(8\) to both sides:

\[
y = -2x + 16
\]

The slope (\(m\)) of line \(g\) is \(-2\). Since line \(h\) is parallel to line \(g\), it will have the same slope of \(-2\).

Now, we need to find the equation of line \(h\) that passes through the point \((-5, 1)\). We can use the point-slope form of a line equation, which is:

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

Substituting in \(m = -2\) and the point \((-5, 1)\):

\[
y - 1 = -2(x - (-5))
\]

This simplifies to:

\[
y - 1 = -2(x + 5)
\]

Distributing \(-2\):

\[
y - 1 = -2x - 10
\]

Adding \(1\) to both sides gives us:

\[
y = -2x - 9
\]

Thus, the equation of line \(h\) in slope-intercept form is:

\[
\boxed{y = -2x - 9}
\]