Question

A line has a slope of
–
1
5
and passes through the point (
–
5,7). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

To find the equation of the line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can use the given slope and point.

The slope \( m \) is given as \( -\frac{1}{5} \) and the line passes through the point \( (-5, 7) \). Using this information, we can substitute these values into the point-slope form of the equation, which is:

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

Substituting \( m = -\frac{1}{5} \), \( x_1 = -5 \), and \( y_1 = 7 \):

\[
y - 7 = -\frac{1}{5}(x - (-5))
\]

This simplifies to:

\[
y - 7 = -\frac{1}{5}(x + 5)
\]

Now distribute \( -\frac{1}{5} \):

\[
y - 7 = -\frac{1}{5}x - 1
\]

Next, add 7 to both sides to solve for \( y \):

\[
y = -\frac{1}{5}x - 1 + 7
\]

\[
y = -\frac{1}{5}x + 6
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = -\frac{1}{5}x + 6
\]