x+2y=6

Subtract x from both sides of the equation.

2y=6-x

Divide each term by 2 and simplify.

Divide each term in 2y=6-x by 2.

2y2=62+-x2

Cancel the common factor of 2.

Cancel the common factor.

2y2=62+-x2

Divide y by 1.

y=62+-x2

y=62+-x2

Simplify each term.

Divide 6 by 2.

y=3+-x2

Move the negative in front of the fraction.

y=3-x2

y=3-x2

y=3-x2

y=3-x2

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 -x2.

y=-x2+3

Rewrite in slope-intercept form.

y=-12x+3

y=-12x+3

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

m=-12

b=3

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

Slope: -12

y-intercept: 3

Slope: -12

y-intercept: 3

Choose 2 to substitute in for x to find the ordered pair.

Replace the variable x with 2 in the expression.

f(2)=-22+3

Simplify the result.

Simplify each term.

Divide 2 by 2.

f(2)=-1⋅1+3

Multiply -1 by 1.

f(2)=-1+3

f(2)=-1+3

Add -1 and 3.

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)=-02+3

Simplify the result.

Simplify each term.

Divide 0 by 2.

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

Create a table of the x and y values.

xy0322

xy0322

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

Slope: -12

y-intercept: 3

xy0322

Graph x+2y=6