The equation for line g can be written as y–8=

Question

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2(x–4). Line h is parallel to line g and passes through (
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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:

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