Question

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

Answer 1

To write the equation of a line in slope-intercept form, we can use the formula:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

We are given:
- Slope \( m = 7 \)
- A point on the line \( (-1, -8) \)

First, we can substitute the slope and the point into the equation to solve for \( b \).

Start with the equation:

\[
y = 7x + b
\]

Substituting \( x = -1 \) and \( y = -8 \):

\[
-8 = 7(-1) + b
\]

Calculating the right-hand side:

\[
-8 = -7 + b
\]

Now, we add 7 to both sides to solve for \( b \):

\[
-8 + 7 = b
\]
\[
b = -1
\]

Now that we have \( b \), we can write the equation of the line:

\[
y = 7x - 1
\]

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

\[
\boxed{y = 7x - 1}
\]