Question

An equation is shown.

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

The point ((5,6), (-5,-6), (6,5), (0,0), or (-6,5)
is on the graph of the line.

Answer 1

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

1. Distribute \(-3\) on the right side:

\[
y - 5 = -3x - 18
\]

2. Add \(5\) to both sides to isolate \(y\):

\[
y = -3x - 18 + 5
\]

3. Simplify the right side:

\[
y = -3x - 13
\]

So, the equation in slope-intercept form is:

\[
y = -3x - 13
\]

Next, we can check which of the points provided is on the graph of the line by substituting each point's coordinates into the equation \(y = -3x - 13\).

1. For \((5, 6)\):
\[
y = -3(5) - 13 = -15 - 13 = -28 \quad (\text{not on the line})
\]

2. For \((-5, -6)\):
\[
y = -3(-5) - 13 = 15 - 13 = 2 \quad (\text{not on the line})
\]

3. For \((6, 5)\):
\[
y = -3(6) - 13 = -18 - 13 = -31 \quad (\text{not on the line})
\]

4. For \((0, 0)\):
\[
y = -3(0) - 13 = 0 - 13 = -13 \quad (\text{not on the line})
\]

5. For \((-6, 5)\):
\[
y = -3(-6) - 13 = 18 - 13 = 5 \quad (\text{this point is on the line})
\]

Thus, the point on the graph of the line is \((-6, 5)\).

### Final Answers:
- The equation in slope-intercept form is: **\( y = -3x - 13 \)**
- The point on the graph of the line is: **\((-6, 5)\)**.