# Graph x+3y=9 x+3y=9
Solve for y.
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
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 3 and -x3.
y=-x3+3
Rewrite in slope-intercept form.
y=-13x+3
y=-13x+3
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=-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
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 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
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