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−2
y equals negative x minus 2

y=x−1
y equals x minus 1

y=−x+3

Answer 1

To write the equation of a line in slope-intercept form (y = mx + b), we need to identify the slope (m) and the y-intercept (b).

Given:
- The slope (m) is -1.
- The line passes through the point (-5, 3).

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

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

Here, \((x_1, y_1)\) is the point \((-5, 3)\).

Substituting in the values:

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

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**.