To graph the equation 3x + 5y = 15, follow these steps:
Step 1: Rearrange the Equation
First, it helps to rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. To do this, solve for y:
5y = -3x + 15
y = - rac{3}{5}x + 3
Step 2: Identify the Slope and Y-Intercept
From the rearranged equation y = - rac{3}{5}x + 3, we can identify:
- Slope (m): -3/5 (This means that for every 5 units you move to the right on the x-axis, you’ll move 3 units down on the y-axis.)
- Y-Intercept (b): 3 (This means the graph crosses the y-axis at the point (0, 3).)
Step 3: Find the X-Intercept
To find the x-intercept, set y = 0 in the original equation:
3x + 5(0) = 15 3x = 15 x = 5
This means the graph crosses the x-axis at the point (5, 0).
Step 4: Plot the Points
Now that we have both intercepts, we can plot these points on a graph:
- Y-Intercept: (0, 3)
- X-Intercept: (5, 0)
Step 5: Draw the Graph
Using a ruler, draw a straight line through these two points. This line represents the graph of the equation 3x + 5y = 15. The line will slope downwards from left to right, reflecting the negative slope of -3/5.
Conclusion
When you graph the equation, you’ll visually see how 3x + 5y = 15 relates x and y values, demonstrating all the possible solutions to this linear equation. You can also use additional points for accuracy, but the two intercepts will suffice to illustrate the line accurately.