How do you graph 2x – 3y + 15 = 0?

To graph the equation 2x – 3y + 15 = 0, follow these steps:

Rewrite the equation in slope-intercept form (y = mx + b), which makes it easier to graph. Start by isolating y:

2x – 3y + 15 = 0
Subtract 2x from both sides:
-3y = -2x - 15
Divide both sides by -3:
y = (2/3)x + 5

Now we have the equation in slope-intercept form:
y = (2/3)x + 5

Identify the slope (m) and y-intercept (b):

The slope (m) is 2/3, meaning for every 3 units you move to the right (along the x-axis), you move 2 units up (along the y-axis).
The y-intercept (b) is 5, meaning the line crosses the y-axis at the point (0, 5).
Plot the y-intercept:
Start by plotting the point (0, 5) on the graph, where the line crosses the y-axis.

Use the slope to find another point:
From the point (0, 5), use the slope (2/3) to find another point. Move 3 units to the right (along the x-axis) and 2 units up (along the y-axis). This gives you the point (3, 7).

Draw the line:
Plot both points, (0, 5) and (3, 7), on the graph. Then draw a straight line through these points. This line represents the equation 2x – 3y + 15 = 0.

In summary:

The slope is 2/3.
The y-intercept is 5.
The graph is a straight line that crosses the y-axis at (0, 5) and passes through (3, 7).