# Graph 9x-3y=-6 9x-3y=-6
Solve for y.
Subtract 9x from both sides of the equation.
-3y=-6-9x
Divide each term by -3 and simplify.
Divide each term in -3y=-6-9x by -3.
-3y-3=-6-3+-9x-3
Cancel the common factor of -3.
Cancel the common factor.
-3y-3=-6-3+-9x-3
Divide y by 1.
y=-6-3+-9x-3
y=-6-3+-9x-3
Simplify each term.
Divide -6 by -3.
y=2+-9x-3
Cancel the common factor of -9 and -3.
Factor -3 out of -9x.
y=2+-3(3x)-3
Cancel the common factors.
Factor -3 out of -3.
y=2+-3(3x)-3(1)
Cancel the common factor.
y=2+-3(3x)-3⋅1
Rewrite the expression.
y=2+3×1
Divide 3x by 1.
y=2+3x
y=2+3x
y=2+3x
y=2+3x
y=2+3x
y=2+3x
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 2 and 3x.
y=3x+2
y=3x+2
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=3
b=2
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: 3
y-intercept: 2
Slope: 3
y-intercept: 2
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)=3(0)+2
Simplify the result.
Multiply 3 by 0.
f(0)=0+2
f(0)=2
2
2
The y value at x=0 is 2.
y=2
y=2
Choose 1 to substitute in for x to find the ordered pair.
Replace the variable x with 1 in the expression.
f(1)=3(1)+2
Simplify the result.
Multiply 3 by 1.
f(1)=3+2
f(1)=5
5
5
The y value at x=1 is 5.
y=5
y=5
Create a table of the x and y values.
xy0215
xy0215
Graph the line using the slope and the y-intercept, or the points.
Slope: 3
y-intercept: 2
xy0215
Graph 9x-3y=-6     