Here we will show you how to calculate and provide solutions to math problems related to 3x - 4y = 14.
We will start by calculating and showing you the solution for the x-intercept and y-intercept of 3x - 4y = 14.
Then, we will show you how to get the graph plot coordinates for 3x - 4y = 14 so we can illustrate it on a graph.
Finally, we will solve 3x - 4y = 14 for x and also for y, then calculate and show you the solution for the slope of 3x - 4y = 14.
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 = 14
3x - 4(0) = 14
x1 = 4.667 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 = 14
3(0) - 4y = 14
y2 = -3.5 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 3x - 4y = 14 as follows:
(x1,y1) and (x2,y2)
(4.667,0) and (0,-3.5)
Solve for x
To solve for x, we solve the equation so the variable x is by itself on the left side:
3x - 4y = 14
x = 1.333y + 4.667
Solve for y
To solve for y, we solve the equation so the variable y is by itself on the left side:
3x - 4y = 14
y = 0.75x - 3.5
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 3x - 4y = 14
m = (y2 - y1)/(x2 - x1)
m = (-3.5 - 0)/(0 - 4.667)
m = 0.75
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