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−1
y equals x minus 1

y=−x−2
y equals negative x minus 2

y=−x+3
y equals negative x plus 3

y=−x−5

Answer 1

To find the equation of a line in slope-intercept form (y = mx + b) that passes through the point (−5, 3) and has a slope of −1, we can follow these steps:

1. **Identify the slope (m)**: Given as −1.
2. **Use the point (−5, 3)**: Here, x = −5 and y = 3.
3. **Plug the values into the slope-intercept equation**:

Starting with the general form:
\[ y = mx + b \]

Substituting the slope:
\[ y = -1x + b \]
or
\[ y = -x + b \]

Now, use the point (−5, 3) to find b (the y-intercept):
\[ 3 = -(-5) + b \]
\[ 3 = 5 + b \]

Now, solve for b:
\[ b = 3 - 5 \]
\[ b = -2 \]

So, the equation of the line in slope-intercept form is:
\[ y = -x - 2 \]

The correct response is:
**y = −x − 2** (y equals negative x minus 2).