x+3y=9

Subtract x from both sides of the equation.

3y=9-x

Divide each term by 3 and simplify.

Divide each term in 3y=9-x by 3.

3y3=93+-x3

Cancel the common factor of 3.

Cancel the common factor.

3y3=93+-x3

Divide y by 1.

y=93+-x3

y=93+-x3

Simplify each term.

Divide 9 by 3.

y=3+-x3

Move the negative in front of the fraction.

y=3-x3

y=3-x3

y=3-x3

y=3-x3

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

y=mx+b

Reorder 3 and -x3.

y=-x3+3

Rewrite in slope-intercept form.

y=-13x+3

y=-13x+3

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

m=-13

b=3

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

Slope: -13

y-intercept: 3

Slope: -13

y-intercept: 3

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

Replace the variable x with 0 in the expression.

f(0)=-03+3

Simplify the result.

Simplify each term.

Divide 0 by 3.

f(0)=-0+3

Multiply -1 by 0.

f(0)=0+3

f(0)=0+3

Add 0 and 3.

f(0)=3

The final answer is 3.

3

3

The y value at x=0 is 3.

y=3

y=3

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

Replace the variable x with 3 in the expression.

f(3)=-33+3

Simplify the result.

Simplify each term.

Divide 3 by 3.

f(3)=-1⋅1+3

Multiply -1 by 1.

f(3)=-1+3

f(3)=-1+3

Add -1 and 3.

f(3)=2

The final answer is 2.

2

2

The y value at x=3 is 2.

y=2

y=2

Create a table of the x and y values.

xy0332

xy0332

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

Slope: -13

y-intercept: 3

xy0332

Graph x+3y=9