Graph Using a Table of Values y=-3/4x+4

$y = - \frac{3}{4} x + 4$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = - \frac{3}{4} \cdot - 2 + 4$

Step 2

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{3}{4} \cdot - 2 + 4$

Simplify $- \frac{3}{4} \cdot - 2 + 4$ .

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$y = \frac{- 3}{4} \cdot - 2 + 4$

Factor $2$ out of $4$ .

$y = \frac{- 3}{2 (2)} \cdot - 2 + 4$

Factor $2$ out of $- 2$ .

$y = \frac{- 3}{2 \cdot 2} \cdot (2 \cdot - 1) + 4$

Cancel the common factor.

$y = \frac{- 3}{2 \cdot 2} \cdot (2 \cdot - 1) + 4$

Rewrite the expression.

$y = \frac{- 3}{2} \cdot - 1 + 4$

Combine $\frac{- 3}{2}$ and $- 1$ .

$y = \frac{- 3 \cdot - 1}{2} + 4$

Multiply $- 3$ by $- 1$ .

$y = \frac{3}{2} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{3}{2} + 4 \cdot \frac{2}{2}$

Combine $4$ and $\frac{2}{2}$ .

$y = \frac{3}{2} + \frac{4 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{3 + 4 \cdot 2}{2}$

Simplify the numerator.

Multiply $4$ by $2$ .

$y = \frac{3 + 8}{2}$

Add $3$ and $8$ .

$y = \frac{11}{2}$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = - \frac{3}{4} \cdot - 1 + 4$

Step 4

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{3}{4} \cdot - 1 + 4$

Simplify $- \frac{3}{4} \cdot - 1 + 4$ .

Multiply $- \frac{3}{4} \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$y = 1 (\frac{3}{4}) + 4$

Multiply $\frac{3}{4}$ by $1$ .

$y = \frac{3}{4} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{3}{4} + 4 \cdot \frac{4}{4}$

Combine $4$ and $\frac{4}{4}$ .

$y = \frac{3}{4} + \frac{4 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{3 + 4 \cdot 4}{4}$

Simplify the numerator.

Multiply $4$ by $4$ .

$y = \frac{3 + 16}{4}$

Add $3$ and $16$ .

$y = \frac{19}{4}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = - \frac{3}{4} \cdot 0 + 4$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{3}{4} \cdot 0 + 4$

Simplify $- \frac{3}{4} \cdot 0 + 4$ .

Multiply $- \frac{3}{4} \cdot 0$ .

Multiply $0$ by $- 1$ .

$y = 0 (\frac{3}{4}) + 4$

Multiply $0$ by $\frac{3}{4}$ .

$y = 0 + 4$

Add $0$ and $4$ .

$y = 4$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = - \frac{3}{4} \cdot 1 + 4$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{3}{4} \cdot 1 + 4$

Simplify $- \frac{3}{4} \cdot 1 + 4$ .

Multiply $- 1$ by $1$ .

$y = - \frac{3}{4} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{3}{4} + 4 \cdot \frac{4}{4}$

Combine $4$ and $\frac{4}{4}$ .

$y = - \frac{3}{4} + \frac{4 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{- 3 + 4 \cdot 4}{4}$

Simplify the numerator.

Multiply $4$ by $4$ .

$y = \frac{- 3 + 16}{4}$

Add $- 3$ and $16$ .

$y = \frac{13}{4}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = - \frac{3}{4} \cdot 2 + 4$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = - \frac{3}{4} \cdot 2 + 4$

Simplify $- \frac{3}{4} \cdot 2 + 4$ .

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$y = \frac{- 3}{4} \cdot 2 + 4$

Factor $2$ out of $4$ .

$y = \frac{- 3}{2 (2)} \cdot 2 + 4$

Cancel the common factor.

$y = \frac{- 3}{2 \cdot 2} \cdot 2 + 4$

Rewrite the expression.

$y = \frac{- 3}{2} + 4$

Move the negative in front of the fraction.

$y = - \frac{3}{2} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{3}{2} + 4 \cdot \frac{2}{2}$

Combine $4$ and $\frac{2}{2}$ .

$y = - \frac{3}{2} + \frac{4 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{- 3 + 4 \cdot 2}{2}$

Simplify the numerator.

Multiply $4$ by $2$ .

$y = \frac{- 3 + 8}{2}$

Add $- 3$ and $8$ .

$y = \frac{5}{2}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & \frac{11}{2} \\ - 1 & \frac{19}{4} \\ 0 & 4 \\ 1 & \frac{13}{4} \\ 2 & \frac{5}{2} \end{array}$

Step 12

Graph Using a Table of Values y=-3/4x+4

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