x - 3y = 23

Here we will show you how to calculate and provide solutions to math problems related to x - 3y = 23.

We will start by calculating and showing you the solution for the x-intercept and y-intercept of x - 3y = 23.

Then, we will show you how to get the graph plot coordinates for x - 3y = 23 so we can illustrate it on a graph.

Finally, we will solve x - 3y = 23 for x and also for y, then calculate and show you the solution for the slope of x - 3y = 23.

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.

x - 3y = 23
x - 3(0) = 23
x₁ = 23 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.

x - 3y = 23
1(0) - 3y = 23
y₂ = -7.667 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 x - 3y = 23 as follows:

(x₁,y₁) and (x₂,y₂)
(23,0) and (0,-7.667)

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

x - 3y = 23
x = 3y + 23

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

x - 3y = 23
y = 0.333x - 7.667

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 x - 3y = 23

m = (y₂ - y₁)/(x₂ - x₁)
m = (-7.667 - 0)/(0 - 23)
m = 0.333

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