4x-6y=36

Subtract 4x from both sides of the equation.

-6y=36-4x

Divide each term by -6 and simplify.

Divide each term in -6y=36-4x by -6.

-6y-6=36-6+-4x-6

Cancel the common factor of -6.

Cancel the common factor.

-6y-6=36-6+-4x-6

Divide y by 1.

y=36-6+-4x-6

y=36-6+-4x-6

Simplify each term.

Divide 36 by -6.

y=-6+-4x-6

Cancel the common factor of -4 and -6.

Factor -2 out of -4x.

y=-6+-2(2x)-6

Cancel the common factors.

Factor -2 out of -6.

y=-6+-2(2x)-2(3)

Cancel the common factor.

y=-6+-2(2x)-2⋅3

Rewrite the expression.

y=-6+2×3

y=-6+2×3

y=-6+2×3

y=-6+2×3

y=-6+2×3

y=-6+2×3

The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Reorder -6 and 2×3.

y=2×3-6

Rewrite in slope-intercept form.

y=23x-6

y=23x-6

Find the values of m and b using the form y=mx+b.

m=23

b=-6

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: 23

y-intercept: -6

Slope: 23

y-intercept: -6

Choose 3 to substitute in for x to find the ordered pair.

Replace the variable x with 3 in the expression.

f(3)=2(3)3-6

Simplify the result.

Multiply 2 by 3.

f(3)=63-6

Divide 6 by 3.

f(3)=2-6

Subtract 6 from 2.

f(3)=-4

The final answer is -4.

-4

-4

The y value at x=3 is -4.

y=-4

y=-4

Choose 0 to substitute in for x to find the ordered pair.

Replace the variable x with 0 in the expression.

f(0)=2(0)3-6

Simplify the result.

Multiply 2 by 0.

f(0)=03-6

Divide 0 by 3.

f(0)=0-6

Subtract 6 from 0.

f(0)=-6

The final answer is -6.

-6

-6

The y value at x=0 is -6.

y=-6

y=-6

Create a table of the x and y values.

xy0-63-4

xy0-63-4

Graph the line using the slope and the y-intercept, or the points.

Slope: 23

y-intercept: -6

xy0-63-4

Graph 4x-6y=36