Here we will show you how to calculate and provide solutions to math problems related to 4x - 8y = 21.
We will start by calculating and showing you the solution for the x-intercept and y-intercept of 4x - 8y = 21.
Then, we will show you how to get the graph plot coordinates for 4x - 8y = 21 so we can illustrate it on a graph.
Finally, we will solve 4x - 8y = 21 for x and also for y, then calculate and show you the solution for the slope of 4x - 8y = 21.
Find x-intercept
The x-intercept is where the graph crosses the x-axis. To find the x-intercept, we set y1=0 and then solve for x.
4x - 8y = 21
4x - 8(0) = 21
x1 = 5.25 y1 = 0
Find y-intercept
The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.
4x - 8y = 21
4(0) - 8y = 21
y2 = -2.625 x2 = 0
Get Graph Plot Coordinates
Getting two graph points will allow you to make a straight line on a graph. The plot coordinate format is (x1,y1) and (x2,y2).
Thus, we use the x-intercept and y-intercept results above to get the graph plots for 4x - 8y = 21 as follows:
(x1,y1) and (x2,y2)
(5.25,0) and (0,-2.625)
Solve for x
To solve for x, we solve the equation so the variable x is by itself on the left side:
4x - 8y = 21
x = 2y + 5.25
Solve for y
To solve for y, we solve the equation so the variable y is by itself on the left side:
4x - 8y = 21
y = 0.5x - 2.625
Find slope
The slope of the line (m) is the steepness of the line. It is the change in the y coordinate divided by the corresponding change in the x coordinate. Simply plug in the coordinates from above and solve for m to get the slope for 4x - 8y = 21
m = (y2 - y1)/(x2 - x1)
m = (-2.625 - 0)/(0 - 5.25)
m = 0.5
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