Question

Graph this line:
y–3=
–
2(x+4)
Click to select points on the graph.

Answer 1

To graph the line given by the equation \( y - 3 = -2(x + 4) \), we can start by rewriting it in slope-intercept form \( y = mx + b \).

1. Start with the original equation:
\[
y - 3 = -2(x + 4)
\]

2. Distribute \(-2\):
\[
y - 3 = -2x - 8
\]

3. Add \(3\) to both sides to solve for \(y\):
\[
y = -2x - 8 + 3
\]
\[
y = -2x - 5
\]

Now we have the equation in slope-intercept form \( y = -2x - 5 \), where the slope \( m = -2 \) and the y-intercept \( b = -5 \).

### Graphing Steps:
1. **Plot the y-intercept**: Start by plotting the point \( (0, -5) \) on the graph.
2. **Use the slope**: From the y-intercept, use the slope to find another point. The slope of \(-2\) means you go down \(2\) units and to the right \(1\) unit:
- From \( (0, -5) \), move down to \( (1, -7) \).
3. **Draw the line**: Draw a straight line through the points you plotted.

### Summary of Points:
- Y-intercept: \( (0, -5) \)
- Second point: \( (1, -7) \)

You can also find more points by choosing different values of \(x\), but using just these two points is enough to graph the line accurately.

If you have graphing tools, you can plot these points and draw the line accordingly!