3x + 4y = 13

Here we will show you how to calculate and provide solutions to math problems related to 3x + 4y = 13.

We will start by calculating and showing you the solution for the x-intercept and y-intercept of 3x + 4y = 13.

Then, we will show you how to get the graph plot coordinates for 3x + 4y = 13 so we can illustrate it on a graph.

Finally, we will solve 3x + 4y = 13 for x and also for y, then calculate and show you the solution for the slope of 3x + 4y = 13.

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.

3x + 4y = 13
3x + 4(0) = 13
x₁ = 4.333 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.

3x + 4y = 13
3(0) + 4y = 13
y₂ = 3.25 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 3x + 4y = 13 as follows:

(x₁,y₁) and (x₂,y₂)
(4.333,0) and (0,3.25)

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

3x + 4y = 13
x = 4.333 - 1.333y

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

3x + 4y = 13
y = 3.25 - 0.75x

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 3x + 4y = 13

m = (y₂ - y₁)/(x₂ - x₁)
m = (3.25 - 0)/(0 - 4.333)
m = -0.75

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