Question

Graph these equations:
3x–5y=15
3x–5y=15
Click to select points on the graph.

Answer 1

To graph the equation \(3x - 5y = 15\), we can first rearrange it into slope-intercept form, which is \(y = mx + b\).

1. Start with the equation:
\[
3x - 5y = 15
\]

2. Rearranging to isolate \(y\):
\[
-5y = -3x + 15
\]

3. Dividing each term by \(-5\):
\[
y = \frac{3}{5}x - 3
\]

Now we can identify the slope and y-intercept:
- The slope \(m\) is \(\frac{3}{5}\), which means for every 5 units we move to the right (positive x-direction), we move 3 units up (positive y-direction).
- The y-intercept \(b\) is -3, which means the line crosses the y-axis at (0, -3).

### Plotting Steps:
1. **Y-Intercept**: Start at the point (0, -3) on the graph.
2. **Using the Slope**: From (0, -3), move right 5 units and up 3 units to reach the point (5, 0).
3. **Repeat the Slope**: From (5, 0), move right 5 units and up 3 units to reach the point (10, 3).
4. You can also move in the opposite direction. From (0, -3), move left 5 units and down 3 units to reach (-5, -6).

### Drawing the Line:
Once you have plotted the points (0, -3), (5, 0), and (10, 3) on the graph, you can connect these points with a straight line extending in both directions.

Now you can graph the line representing the equation \(3x - 5y = 15\).