Question

The equation y minus 3 = negative 2 (x + 5) is written in point-slope form. What is the y-intercept of the line?
–13
–7
2
8

Answer 1

To find the y-intercept of the line given in point-slope form, we first need to rewrite the equation in slope-intercept form (which is \(y = mx + b\), where \(b\) is the y-intercept).

Starting with the provided equation:
\[
y - 3 = -2(x + 5)
\]

We first distribute the \(-2\) on the right side:
\[
y - 3 = -2x - 10
\]

Next, we add 3 to both sides to solve for \(y\):
\[
y = -2x - 10 + 3
\]
\[
y = -2x - 7
\]

Now, we can clearly see that the slope is \(-2\) and the y-intercept \(b\) is \(-7\).

Thus, the y-intercept of the line is \(\boxed{-7}\).