6x - 7y = 89

Here we will show you how to calculate and provide solutions to math problems related to 6x - 7y = 89.

We will start by calculating and showing you the solution for the x-intercept and y-intercept of 6x - 7y = 89.

Then, we will show you how to get the graph plot coordinates for 6x - 7y = 89 so we can illustrate it on a graph.

Finally, we will solve 6x - 7y = 89 for x and also for y, then calculate and show you the solution for the slope of 6x - 7y = 89.

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 - 7y = 89
6x - 7(0) = 89
x₁ = 14.833 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 - 7y = 89
6(0) - 7y = 89
y₂ = -12.714 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 - 7y = 89 as follows:

(x₁,y₁) and (x₂,y₂)
(14.833,0) and (0,-12.714)

Solve for x
To solve for x, we solve the equation so the variable x is by itself on the left side:

6x - 7y = 89
x = 1.167y + 14.833

Solve for y
To solve for y, we solve the equation so the variable y is by itself on the left side:

6x - 7y = 89
y = 0.857x - 12.714

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 - 7y = 89

m = (y₂ - y₁)/(x₂ - x₁)
m = (-12.714 - 0)/(0 - 14.833)
m = 0.857

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