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−5
y equals negative x minus 5

y=x−1
y equals x minus 1

y=−x+3
y equals negative x plus 3

y=−x−2

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we start with the slope and a point. The slope (m) is given as -1, and the point is (-5, 3).

We can use the point-slope form of the equation of a line, which is:

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

Substituting the values:

- \( m = -1 \)
- \( x_1 = -5 \)
- \( y_1 = 3 \)

The equation becomes:

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

Now, simplify the equation:

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

Adding 3 to both sides:

\[ y = -x - 5 + 3 \]
\[ y = -x - 2 \]

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

**y = -x - 2**

So the correct response is:

y = −x − 2.