9x+6y=-14

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

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

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

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

The final answer is -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

The final answer is -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