# Graph -x+4y=10

-x+4y=10
Solve for y.
Add x to both sides of the equation.
4y=10+x
Divide each term by 4 and simplify.
Divide each term in 4y=10+x by 4.
4y4=104+x4
Cancel the common factor of 4.
Cancel the common factor.
4y4=104+x4
Divide y by 1.
y=104+x4
y=104+x4
Cancel the common factor of 10 and 4.
Factor 2 out of 10.
y=2(5)4+x4
Cancel the common factors.
Factor 2 out of 4.
y=2⋅52⋅2+x4
Cancel the common factor.
y=2⋅52⋅2+x4
Rewrite the expression.
y=52+x4
y=52+x4
y=52+x4
y=52+x4
y=52+x4
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 52 and x4.
y=x4+52
Rewrite in slope-intercept form.
y=14x+52
y=14x+52
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=14
b=52
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: 14
y-intercept: 52
Slope: 14
y-intercept: 52
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 2 to substitute in for x to find the ordered pair.
Replace the variable x with 2 in the expression.
f(2)=24+52
Simplify the result.
Cancel the common factor of 2 and 4.
Factor 2 out of 2.
f(2)=2(1)4+52
Cancel the common factors.
Factor 2 out of 4.
f(2)=2⋅12⋅2+52
Cancel the common factor.
f(2)=2⋅12⋅2+52
Rewrite the expression.
f(2)=12+52
f(2)=12+52
f(2)=12+52
Combine the numerators over the common denominator.
f(2)=1+52
f(2)=62
Divide 6 by 2.
f(2)=3
3
3
The y value at x=2 is 3.
y=3
y=3
Choose 0 to substitute in for x to find the ordered pair.
Replace the variable x with 0 in the expression.
f(0)=04+52
Simplify the result.
Divide 0 by 4.
f(0)=0+52
f(0)=52
52
52
The y value at x=0 is 52.
y=52
y=52
Create a table of the x and y values.
xy05223
xy05223
Graph the line using the slope and the y-intercept, or the points.
Slope: 14
y-intercept: 52
xy05223
Graph -x+4y=10