The equation 4x + 5y = 15 is a linear equation in two variables, which can be represented graphically as a straight line on a Cartesian plane.
To graph this equation, we can rewrite it in slope-intercept form (y = mx + b). First, we’ll isolate y:
5y = 15 - 4xy = -\frac{4}{5}x + 3From this form, we can see that the slope (m) is -4/5 and the y-intercept (b) is 3. This means that the line crosses the y-axis at the point (0, 3) and has a slope that indicates it will rise 4 units for every 5 units it moves to the right.
To plot the graph, we can start by marking the y-intercept at (0, 3). From there, we can use the slope to find another point: if we move 5 units to the right (to x = 5), we will move 4 units down, leading us to (5, -1). Connecting these two points will give us the graph of the equation.
Overall, the graph of the equation 4x + 5y = 15 is a straight line that slopes downwards from left to right, intersecting the y-axis at (0, 3) and the x-axis at (3.75, 0) when further calculated.