Find the x- and y-intercepts for the equation. Please show all of your work. Then graph the equation
2x + 3y = 15
to get the x-intercept, we set y = 0 and solve for x:
2x + 3y = 15
2x + 3(0) = 15
2x = 15
x = 7.5
thus, x-intercept is at (7.5, 0)
to get y-intercept, we set x = 0 and solve for y:
2x + 3y = 15
2(0) + 3y = 15
3y = 15
y = 5
thus, y-intercept is at (0, 5)
to plot this, locate the x- and y-intercept, which are the points we solved above. then connect these points and extend on both ends.
hope this helps~ :)
To find the x-intercept, we set y = 0 and solve for x.
Substituting y = 0 into the equation 2x + 3y = 15, we get:
2x + 3(0) = 15
Simplifying the equation, we have:
2x + 0 = 15
Therefore, 2x = 15
Dividing both sides of the equation by 2, we find:
x = 15/2
So, the x-intercept is x = 15/2 or x = 7.5.
To find the y-intercept, we set x = 0 and solve for y.
Substituting x = 0 into the equation 2x + 3y = 15, we get:
2(0) + 3y = 15
Simplifying the equation, we have:
0 + 3y = 15
Therefore, 3y = 15
Dividing both sides of the equation by 3, we find:
y = 15/3
So, the y-intercept is y = 15/3 or y = 5.
Now, let's graph the equation.
To do this, we can plot the x- and y-intercepts on the coordinate plane.
The x-intercept (7.5, 0) means that the line intersects the x-axis at the point (7.5, 0).
The y-intercept (0, 5) means that the line intersects the y-axis at the point (0, 5).
We can plot these two points on the coordinate plane and then draw a straight line passing through them to represent the equation.
I apologize for not being able to provide a visual graph as I am a text-based AI. However, you can manually plot the points (7.5, 0) and (0, 5) on a graph paper and connect them with a straight line to graph the equation.