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?

Answer 1

To write the equation of a line in slope-intercept form (y = mx + b), we need to use the slope (m) and the y-intercept (b). We already know that the slope (m) is -1 and the line passes through the point (-5, 3).

1. Start with the slope-intercept form:
\[
y = mx + b
\]

2. Substitute the slope into the equation:
\[
y = -1x + b
\]

3. Now, we need to find the y-intercept (b). We can do this by substituting the coordinates of the point (-5, 3) into the equation:
\[
3 = -1(-5) + b
\]

4. Simplify the equation:
\[
3 = 5 + b
\]

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

6. Now we can rewrite the equation using the slope and the y-intercept:
\[
y = -1x - 2
\]

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