Question

A line has a slope of
–
7 and passes through the point (2,7). 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 a line in slope-intercept form \( y = mx + b \), we start with the slope \( m \) and a point that the line passes through.

Given:
- Slope \( m = -7 \)
- Point \( (2, 7) \)

We can substitute the slope and the coordinates of the point into the equation and solve for \( b \) (the y-intercept).

1. Use the slope-intercept form:
\[
y = mx + b
\]
Substitute \( m = -7 \) and the point \( (x, y) = (2, 7) \):
\[
7 = -7(2) + b
\]

2. Calculate \( -7(2) \):
\[
7 = -14 + b
\]

3. Add 14 to both sides to solve for \( b \):
\[
7 + 14 = b \quad \Rightarrow \quad b = 21
\]

Now we have both \( m \) and \( b \):
- Slope \( m = -7 \)
- Y-intercept \( b = 21 \)

Thus, the equation in slope-intercept form is:
\[
y = -7x + 21
\]

So, the final answer is:
\[
\boxed{y = -7x + 21}
\]