Here we will show you how to calculate and provide solutions to math problems related to 6x - y = 21.
We will start by calculating and showing you the solution for the x-intercept and y-intercept of 6x - y = 21.
Then, we will show you how to get the graph plot coordinates for 6x - y = 21 so we can illustrate it on a graph.
Finally, we will solve 6x - y = 21 for x and also for y, then calculate and show you the solution for the slope of 6x - y = 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.
6x - y = 21
6x - 1(0) = 21
x1 = 3.5 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.
6x - y = 21
6(0) - y = 21
y2 = -21 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 6x - y = 21 as follows:
(x1,y1) and (x2,y2)
(3.5,0) and (0,-21)
Solve for x
To solve for x, we solve the equation so the variable x is by itself on the left side:
6x - y = 21
x = 0.167y + 3.5
Solve for y
To solve for y, we solve the equation so the variable y is by itself on the left side:
6x - y = 21
y = 6x - 21
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 6x - y = 21
m = (y2 - y1)/(x2 - x1)
m = (-21 - 0)/(0 - 3.5)
m = 6
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