# Graph x+4y=-6

x+4y=-6
Solve for y.
Subtract x from both sides of the equation.
4y=-6-x
Divide each term by 4 and simplify.
Divide each term in 4y=-6-x by 4.
4y4=-64+-x4
Cancel the common factor of 4.
Cancel the common factor.
4y4=-64+-x4
Divide y by 1.
y=-64+-x4
y=-64+-x4
Simplify each term.
Cancel the common factor of -6 and 4.
Factor 2 out of -6.
y=2(-3)4+-x4
Cancel the common factors.
Factor 2 out of 4.
y=2⋅-32⋅2+-x4
Cancel the common factor.
y=2⋅-32⋅2+-x4
Rewrite the expression.
y=-32+-x4
y=-32+-x4
y=-32+-x4
Move the negative in front of the fraction.
y=-32+-x4
Move the negative in front of the fraction.
y=-32-x4
y=-32-x4
y=-32-x4
y=-32-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 -32 and -x4.
y=-x4-32
Rewrite in slope-intercept form.
y=-14x-32
y=-14x-32
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=-32
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: -14
y-intercept: -32
Slope: -14
y-intercept: -32
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)=-24-32
Simplify the result.
Cancel the common factor of 2 and 4.
Factor 2 out of 2.
f(2)=-2(1)4-32
Cancel the common factors.
Factor 2 out of 4.
f(2)=-2⋅12⋅2-32
Cancel the common factor.
f(2)=-2⋅12⋅2-32
Rewrite the expression.
f(2)=-12-32
f(2)=-12-32
f(2)=-12-32
Combine the numerators over the common denominator.
f(2)=-1-32
Subtract 3 from -1.
f(2)=-42
Divide -4 by 2.
f(2)=-2
-2
-2
The y value at x=2 is -2.
y=-2
y=-2
Choose 0 to substitute in for x to find the ordered pair.
Replace the variable x with 0 in the expression.
f(0)=-04-32
Simplify the result.
Simplify each term.
Divide 0 by 4.
f(0)=-0-32
Multiply -1 by 0.
f(0)=0-32
f(0)=0-32
Subtract 32 from 0.
f(0)=-32
-32
-32
The y value at x=0 is -32.
y=-32
y=-32
Create a table of the x and y values.
xy0-322-2
xy0-322-2
Graph the line using the slope and the y-intercept, or the points.
Slope: -14
y-intercept: -32
xy0-322-2
Graph x+4y=-6