Question

A line with m=4
passes through the point (−7,−2)
. What is the equation of the line in slope-intercept form?(1 point)
Responses

y=4x−7
y equals 4 x minus 7

y=−4x−2
y equals negative 4 x minus 2

y=−4x−30
y equals negative 4 x minus 30

y=4x+26

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 \( m = 4 \) and the point \( (-7, -2) \).

1. Start with the slope-intercept form:
\[
y = mx + b
\]
Substituting the slope into the equation gives:
\[
y = 4x + b
\]

2. Now we need to find \( b \). We can do this by substituting the coordinates of the point \( (-7, -2) \) into the equation:
\[
-2 = 4(-7) + b
\]

3. Calculating \( 4(-7) \):
\[
-2 = -28 + b
\]

4. Solving for \( b \):
\[
b = -2 + 28
\]
\[
b = 26
\]

5. Now substitute \( b \) back into the slope-intercept equation:
\[
y = 4x + 26
\]

So, the equation of the line in slope-intercept form is:
\[
y = 4x + 26
\]

The correct response is:
**y=4x+26**.