7x - 6y = 3


Here we will show you how to calculate and provide solutions to math problems related to 7x - 6y = 3.

We will start by calculating and showing you the solution for the x-intercept and y-intercept of 7x - 6y = 3.

Then, we will show you how to get the graph plot coordinates for 7x - 6y = 3 so we can illustrate it on a graph.

Finally, we will solve 7x - 6y = 3 for x and also for y, then calculate and show you the solution for the slope of 7x - 6y = 3.




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.

7x - 6y = 3
7x - 6(0) = 3
x1 = 0.429    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.

7x - 6y = 3
7(0) - 6y = 3
y2 = -0.5    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 7x - 6y = 3 as follows:

(x1,y1) and (x2,y2)
(0.429,0) and (0,-0.5)




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

7x - 6y = 3
x = 0.857y + 0.429

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

7x - 6y = 3
y = 1.167x - 0.5



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 7x - 6y = 3

m = (y2 - y1)/(x2 - x1)
m = (-0.5 - 0)/(0 - 0.429)
m = 1.166

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Answers are rounded to the nearest thousandth if necessary. If you want exact answers instead of rounded answers, then keep the fraction answers when you solve the equations instead of converting them to decimal numbers like we did.


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