Question

Tamara is analyzing a line that passes through the point (−5,3)
and has a slope of −1
. How should she write the equation of the line in slope-intercept form?(1 point)
Responses

y=−x+3
y equals negative x plus 3

y=−x−5
y equals negative x minus 5

y=x−1
y equals x minus 1

y=−x−2

Answer 1

To write the equation of a line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can use the point-slope form of the equation and then rearrange it.

The point-slope form is given by:

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

where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope. Given the point \( (-5, 3) \) and the slope \( -1 \), we plug those values into the formula:

\[
y - 3 = -1(x + 5)
\]

Now let's simplify both sides:

\[
y - 3 = -x - 5
\]

Next, we add 3 to both sides to solve for \( y \):

\[
y = -x - 5 + 3
\]

\[
y = -x - 2
\]

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

\[
\boxed{y = -x - 2}
\]

So the correct response is:

y=−x−2