x+4y=-6

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

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

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

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

The final answer is -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

The final answer is -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