Question

y - 5 = -3(x+6) write in slope intercept form and where is the point on the graph

Answer 1

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

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

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

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

\[
y = -3x - 18 + 5
\]
\[
y = -3x - 13
\]

Now, the equation in slope-intercept form is:

\[
y = -3x - 13
\]

From this equation, we can identify the slope \(m\) and the y-intercept \(b\):

- Slope (\(m\)): \(-3\)
- Y-intercept (\(b\)): \(-13\) (which means the point \( (0, -13) \) is on the graph)

To find a specific point on the graph, you can choose any value for \(x\) and solve for \(y\). For example:

If \(x = 0\),
\[
y = -3(0) - 13 = -13
\]
The point is \( (0, -13) \).

If \(x = 1\),
\[
y = -3(1) - 13 = -3 - 13 = -16
\]
The point is \( (1, -16) \).

Thus, the equation is \( y = -3x - 13 \), and there are multiple points on the graph, including \( (0, -13) \) and \( (1, -16) \).