# Graph 9x+6y=-14

9x+6y=-14
Solve for y.
Subtract 9x from both sides of the equation.
6y=-14-9x
Divide each term by 6 and simplify.
Divide each term in 6y=-14-9x by 6.
6y6=-146+-9×6
Cancel the common factor of 6.
Cancel the common factor.
6y6=-146+-9×6
Divide y by 1.
y=-146+-9×6
y=-146+-9×6
Simplify each term.
Cancel the common factor of -14 and 6.
Factor 2 out of -14.
y=2(-7)6+-9×6
Cancel the common factors.
Factor 2 out of 6.
y=2⋅-72⋅3+-9×6
Cancel the common factor.
y=2⋅-72⋅3+-9×6
Rewrite the expression.
y=-73+-9×6
y=-73+-9×6
y=-73+-9×6
Move the negative in front of the fraction.
y=-73+-9×6
Cancel the common factor of -9 and 6.
Factor 3 out of -9x.
y=-73+3(-3x)6
Cancel the common factors.
Factor 3 out of 6.
y=-73+3(-3x)3(2)
Cancel the common factor.
y=-73+3(-3x)3⋅2
Rewrite the expression.
y=-73+-3×2
y=-73+-3×2
y=-73+-3×2
Move the negative in front of the fraction.
y=-73-3×2
y=-73-3×2
y=-73-3×2
y=-73-3×2
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 -73 and -3×2.
y=-3×2-73
Rewrite in slope-intercept form.
y=-32x-73
y=-32x-73
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=-32
b=-73
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: -32
y-intercept: -73
Slope: -32
y-intercept: -73
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)2-73
Simplify the result.
Simplify each term.
Cancel the common factor of 0 and 2.
Factor 2 out of 3(0).
f(0)=-2(3⋅(0))2-73
Cancel the common factors.
Factor 2 out of 2.
f(0)=-2(3⋅(0))2(1)-73
Cancel the common factor.
f(0)=-2(3⋅(0))2⋅1-73
Rewrite the expression.
f(0)=-3⋅(0)1-73
Divide 3⋅(0) by 1.
f(0)=-(3⋅(0))-73
f(0)=-(3⋅(0))-73
f(0)=-(3⋅(0))-73
Multiply 3 by 0.
f(0)=-0-73
Multiply -1 by 0.
f(0)=0-73
f(0)=0-73
Subtract 73 from 0.
f(0)=-73
-73
-73
The y value at x=0 is -73.
y=-73
y=-73
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)2-73
Simplify the result.
Multiply 3 by 1.
f(1)=-32-73
To write -32 as a fraction with a common denominator, multiply by 33.
f(1)=-32⋅33-73
To write -73 as a fraction with a common denominator, multiply by 22.
f(1)=-32⋅33-73⋅22
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
Multiply 32 and 33.
f(1)=-3⋅32⋅3-73⋅22
Multiply 2 by 3.
f(1)=-3⋅36-73⋅22
Multiply 73 and 22.
f(1)=-3⋅36-7⋅23⋅2
Multiply 3 by 2.
f(1)=-3⋅36-7⋅26
f(1)=-3⋅36-7⋅26
Combine the numerators over the common denominator.
f(1)=-3⋅3-7⋅26
Simplify the numerator.
Multiply -3 by 3.
f(1)=-9-7⋅26
Multiply -7 by 2.
f(1)=-9-146
Subtract 14 from -9.
f(1)=-236
f(1)=-236
Move the negative in front of the fraction.
f(1)=-236
-236
-236
The y value at x=1 is -236.
y=-236
y=-236
Create a table of the x and y values.
xy0-731-236
xy0-731-236
Graph the line using the slope and the y-intercept, or the points.
Slope: -32
y-intercept: -73
xy0-731-236
Graph 9x+6y=-14