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−2
y equals negative 4 x minus 2

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

y=4x−7
y equals 4 x minus 7

y=4x+26

Answer 1

To find the equation of a line in slope-intercept form (which is \(y = mx + b\)) that has a slope \(m=4\) and passes through the point \((-7, -2)\), we follow these steps:

1. Start with the slope-intercept form of the equation:
\[
y = mx + b
\]
Here, \(m = 4\), so we substitute that into the equation:
\[
y = 4x + b
\]

2. Next, we use the point \((-7, -2)\) to find the value of \(b\). Substitute \(x = -7\) and \(y = -2\) into the equation:
\[
-2 = 4(-7) + b
\]

3. Calculate \(4(-7)\):
\[
4(-7) = -28
\]

4. Now substitute this back to solve for \(b\):
\[
-2 = -28 + b
\]
\[
b = -2 + 28
\]
\[
b = 26
\]

5. Now that we have \(b\), we can write the complete equation of the line:
\[
y = 4x + 26
\]

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