y=6-x3

The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Simplify 6-x3.

Split the fraction 6-x3 into two fractions.

y=63+-x3

Simplify each term.

Divide 6 by 3.

y=2+-x3

Move the negative in front of the fraction.

y=2-x3

y=2-x3

Reorder 2 and -x3.

y=-x3+2

y=-x3+2

Rewrite in slope-intercept form.

y=-13x+2

y=-13x+2

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

m=-13

b=2

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

Slope: -13

y-intercept: 2

Slope: -13

y-intercept: 2

Choose 0 to substitute in for x to find the ordered pair.

Replace the variable x with 0 in the expression.

f(0)=6-(0)3

Simplify the result.

Cancel the common factor of 6-(0) and 3.

Rewrite 6 as -1(-6).

f(0)=-1⋅-6-(0)3

Factor -1 out of -1(-6)-(0).

f(0)=-1(-6+0)3

Factor 3 out of -1(-6+0).

f(0)=3(-1(-2+0))3

Cancel the common factors.

Factor 3 out of 3.

f(0)=3(-1(-2+0))3(1)

Cancel the common factor.

f(0)=3(-1(-2+0))3⋅1

Rewrite the expression.

f(0)=-1(-2+0)1

Divide -1(-2+0) by 1.

f(0)=-1(-2+0)

f(0)=-1(-2+0)

f(0)=-1(-2+0)

Simplify the expression.

Rewrite -1(-2+0) as -(-2+0).

f(0)=-(-2+0)

Add -2 and 0.

f(0)=2

Multiply -1 by -2.

f(0)=2

f(0)=2

The final answer is 2.

2

2

The y value at x=0 is 2.

y=2

y=2

Choose 3 to substitute in for x to find the ordered pair.

Replace the variable x with 3 in the expression.

f(3)=6-(3)3

Simplify the result.

Cancel the common factor of 6-(3) and 3.

Rewrite 6 as -1(-6).

f(3)=-1⋅-6-(3)3

Factor -1 out of -1(-6)-(3).

f(3)=-1(-6+3)3

Factor 3 out of -1(-6+3).

f(3)=3(-1(-2+1))3

Cancel the common factors.

Factor 3 out of 3.

f(3)=3(-1(-2+1))3(1)

Cancel the common factor.

f(3)=3(-1(-2+1))3⋅1

Rewrite the expression.

f(3)=-1(-2+1)1

Divide -1(-2+1) by 1.

f(3)=-1(-2+1)

f(3)=-1(-2+1)

f(3)=-1(-2+1)

Simplify the expression.

Rewrite -1(-2+1) as -(-2+1).

f(3)=-(-2+1)

Add -2 and 1.

f(3)=1

Multiply -1 by -1.

f(3)=1

f(3)=1

The final answer is 1.

1

1

The y value at x=3 is 1.

y=1

y=1

Create a table of the x and y values.

xy0231

xy0231

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

Slope: -13

y-intercept: 2

xy0231

Graph y=(6-x)/3