The equation 4x + 5y = 15 represents a linear relationship between the variables x and y. To understand what the graph looks like, we can rewrite the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
First, let’s isolate y:
4x + 5y = 15
5y = 15 - 4x
y = -\frac{4}{5}x + 3Now we can see that:
- The slope (m) is -4/5, which means that for every 5 units you move to the right (positive x), you move 4 units down (negative y).
- The y-intercept (b) is 3, indicating that the line crosses the y-axis at point (0, 3).
To sketch the graph, we can plot the y-intercept first at (0, 3). From there, using the slope of -4/5, we can find another point. For example, moving 5 units to the right from (0, 3) takes us to (5, 3) and then going down 4 units reaches (5, -1).
Connecting these two points gives us a straight line that represents the equation 4x + 5y = 15. The line will extend infinitely in both directions, indicating that there are unlimited (x, y) pairs that satisfy this equation.
You can also find the x-intercept by letting y = 0:
4x + 5(0) = 15
4x = 15
x = \frac{15}{4} = 3.75This point (3.75, 0) can be plotted on the x-axis to further guide your line drawing. Overall, the graph will demonstrate a downward slope that crosses through the y-intercept at (0, 3) and the x-intercept at (3.75, 0). This visual aids in understanding the relationship between x and y in the context of this linear equation.