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+26
y equals 4 x plus 26

y=4x−7
y equals 4 x minus 7

y=−4x−30

Answer 1

To find the equation of a line in slope-intercept form (y = mx + b) that has a slope \( m = 4 \) and passes through the point \( (-7, -2) \), we can start by using the point-slope formula:

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

where \( (x_1, y_1) \) is the point the line passes through.

Substituting \( m = 4 \), \( x_1 = -7 \), and \( y_1 = -2 \) into the formula, we get:

\[
y - (-2) = 4(x - (-7))
\]

This simplifies to:

\[
y + 2 = 4(x + 7)
\]

Now distribute the 4:

\[
y + 2 = 4x + 28
\]

Next, subtract 2 from both sides to solve for \( y \):

\[
y = 4x + 28 - 2
\]
\[
y = 4x + 26
\]

So the equation of the line in slope-intercept form is:

\[
y = 4x + 26
\]

Thus, the correct response is:

**y = 4x + 26**