# Graph 15y-21x=75

15y-21x=75
Solve for y.
Add 21x to both sides of the equation.
15y=75+21x
Divide each term by 15 and simplify.
Divide each term in 15y=75+21x by 15.
15y15=7515+21×15
Cancel the common factor of 15.
Cancel the common factor.
15y15=7515+21×15
Divide y by 1.
y=7515+21×15
y=7515+21×15
Simplify each term.
Divide 75 by 15.
y=5+21×15
Cancel the common factor of 21 and 15.
Factor 3 out of 21x.
y=5+3(7x)15
Cancel the common factors.
Factor 3 out of 15.
y=5+3(7x)3(5)
Cancel the common factor.
y=5+3(7x)3⋅5
Rewrite the expression.
y=5+7×5
y=5+7×5
y=5+7×5
y=5+7×5
y=5+7×5
y=5+7×5
Rewrite in slope-intercept form.
The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Reorder 5 and 7×5.
y=7×5+5
Rewrite in slope-intercept form.
y=75x+5
y=75x+5
Use the slope-intercept form to find the slope and y-intercept.
Find the values of m and b using the form y=mx+b.
m=75
b=5
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: 75
y-intercept: 5
Slope: 75
y-intercept: 5
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
Choose 0 to substitute in for x to find the ordered pair.
Replace the variable x with 0 in the expression.
f(0)=7(0)5+5
Simplify the result.
Multiply 7 by 0.
f(0)=05+5
Divide 0 by 5.
f(0)=0+5
f(0)=5
5
5
The y value at x=0 is 5.
y=5
y=5
Choose 1 to substitute in for x to find the ordered pair.
Replace the variable x with 1 in the expression.
f(1)=7(1)5+5
Simplify the result.
Multiply 7 by 1.
f(1)=75+5
To write 5 as a fraction with a common denominator, multiply by 55.
f(1)=75+5⋅55
Combine 5 and 55.
f(1)=75+5⋅55
Combine the numerators over the common denominator.
f(1)=7+5⋅55
Simplify the numerator.
Multiply 5 by 5.
f(1)=7+255
f(1)=325
f(1)=325
325
325
The y value at x=1 is 325.
y=325
y=325
Create a table of the x and y values.
xy051325
xy051325
Graph the line using the slope and the y-intercept, or the points.
Slope: 75
y-intercept: 5
xy051325
Graph 15y-21x=75