Question

Graph these equations:
2x+3y=
–
12
2x+3y=
–
12
Click to select points on the graph.

Answer 1

It seems like there is a slight confusion in your request as both equations you provided are identical: \( 2x + 3y = -12 \).

To graph the equation \( 2x + 3y = -12 \), we can start by rewriting it in slope-intercept form (y = mx + b):

1. **Isolate y**:
\[
3y = -2x - 12
\]
\[
y = -\frac{2}{3}x - 4
\]

From this form, we can identify the slope (\( m = -\frac{2}{3} \)) and the y-intercept (\( b = -4 \)).

### Steps to Graph:

1. **Plot the y-intercept**:
- Start by plotting the point (0, -4) on the graph.

2. **Use the slope to find another point**:
- From the y-intercept (0, -4), use the slope of \(-\frac{2}{3}\). This means you move down 2 units (because of the negative sign) and to the right 3 units.
- From (0, -4), if you move down 2, you end up at (3, -6).

3. **Draw the line**:
- Connect the points (0, -4) and (3, -6) with a straight line. Extend the line across the graph.

### Additional Points:
If you want to find more points, you can choose other values of x and solve for y. For example:

- If \( x = -3 \):
\[
2(-3) + 3y = -12 \implies -6 + 3y = -12 \implies 3y = -6 \implies y = -2
\]
So, (-3, -2) is another point.

- If \( x = 0 \):
\[
y = -4 \text{ (already plotted)}
\]

- If \( x = 3 \):
\[
2(3) + 3y = -12 \implies 6 + 3y = -12 \implies 3y = -18 \implies y = -6
\]
So, (3, -6) is also plotted.

- Continue to find more points as desired to ensure the line is accurately drawn.

You can click around the graph to select points at various locations along this line. If you need further assistance or examples, let me know!