To graph the equation 15x + 5y = 30, we can start by rearranging it into a more familiar form, such as the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
First, let’s isolate y:
5y = -15x + 30
y = -3x + 6Now the equation is in slope-intercept form. We can see that:
- The slope (m) is -3.
- The y-intercept (b) is 6, which means the line crosses the y-axis at (0, 6).
Next, we can use the slope to find another point on the graph. Starting from the y-intercept (0, 6), we can apply the slope:
- From (0, 6), and using a slope of -3, we move down 3 units and right 1 unit to arrive at the point (1, 3).
Now we have two points: (0, 6) and (1, 3). We can plot these points on our graph:
- Plot the point (0, 6) on the y-axis.
- Plot the point (1, 3).
Next, we can draw a straight line through these points. The line should extend in both directions, and it represents the equation 15x + 5y = 30.
For additional points, you can also substitute values for x to find corresponding y values. For instance:
- If x = 2, then:
y = -3(2) + 6 = 0Continuing this way, you can find more points, but typically plotting two or three is sufficient to get a clear idea of the line’s direction.
In summary, by rearranging the equation, plotting points using the slope, and drawing a line through them, you’ve successfully graphed the original equation 15x + 5y = 30.