Answer:
y = 54 - 5x
Step-by-step explanation:
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5x + y = 54
Here we will show you how to calculate the following:
Calculate and show the solution for the x-intercept and y-intercept of 5x + y = 54.
Calculate the graph plot coordinates for 5x + y = 54
Solve 5x + y = 54 for x and also for y.
Calculate and show the solution for the slope of 5x + y = 54
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.
5x + y = 54
5x + 1(0) = 54
x1 = 10.8 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.
5x + y = 54
5(0) + y = 54
y2 = 54 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 5x + y = 54 as follows:
(x1,y1) and (x2,y2)
(10.8,0) and (0,54)
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 5x + y = 54
m = (y2 - y1)/(x2 - x1)
m = (54 - 0)/(0 - 10.8)
m = -5
Solve for x
To solve for x, we solve the equation so the variable x is by itself on the left side:
5x + y = 54
x = 10.8 - 0.2y
Solve for y
To solve for y, we solve the equation so the variable y is by itself on the left side:
5x + y = 54
y = 54 - 5x
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.
