Question

An equation is shown.

y−5 = −3(x+6)
(2 points)
The equation rewritten in slope-intercept form is

.

The point

is on the graph of the lin

Answer 1

To rewrite the given equation \( y - 5 = -3(x + 6) \) in slope-intercept form (\( y = mx + b \)), we can follow these steps:

1. Distribute the \(-3\) on the right side of the equation:
\[
y - 5 = -3x - 18
\]

2. Add \(5\) to both sides to isolate \(y\):
\[
y = -3x - 18 + 5
\]
\[
y = -3x - 13
\]

Now, the equation in slope-intercept form is:
\[
y = -3x - 13
\]

Next, we need to determine a point that is on the graph of the line. We can select any value for \(x\) and find the corresponding \(y\).

For example, if we let \(x = 0\):
\[
y = -3(0) - 13 = -13
\]
So, the point \((0, -13)\) is on the graph of the line.

In conclusion:
- The equation in slope-intercept form is \(\boxed{y = -3x - 13}\).
- The point \((0, -13)\) is on the graph of the line.