The equation 3x + 5y = 15 represents a straight line in a two-dimensional coordinate system. To graph this equation, we can rearrange it into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let’s solve for y:
5y = 15 - 3x
y = - 3/5 x + 3From this equation, we see that the slope (m) is -3/5 and the y-intercept (b) is 3. This means the line crosses the y-axis at the point (0, 3).
To find another point on the line, we can set x to 0 to find the y-intercept, and set y to 0 to find the x-intercept:
- When x = 0:
5y = 15 → y = 3 (point: (0, 3)) - When y = 0:
3x = 15 → x = 5 (point: (5, 0))
Now we have two points: (0, 3) and (5, 0). Plot these points on a graph and draw a line through them. The line will slope downwards from left to right, reflecting the negative slope.
This is the graph of the equation 3x + 5y = 15.