Graph -3x-y=-10 4x-4y=8

$- 3 x - y = - 10$ $4 x - 4 y = 8$

Step 1

Graph $- 3 x - y = - 10$ .

Solve for $y$ .

Add $3 x$ to both sides of the equation.

$- y = - 10 + 3 x$

Divide each term in $- y = - 10 + 3 x$ by $- 1$ and simplify.

Divide each term in $- y = - 10 + 3 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 10}{- 1} + \frac{3 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 10}{- 1} + \frac{3 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 10}{- 1} + \frac{3 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $- 10$ by $- 1$ .

$y = 10 + \frac{3 x}{- 1}$

Move the negative one from the denominator of $\frac{3 x}{- 1}$ .

$y = 10 - 1 \cdot (3 x)$

Rewrite $- 1 \cdot (3 x)$ as $- (3 x)$ .

$y = 10 - (3 x)$

Multiply $3$ by $- 1$ .

$y = 10 - 3 x$

Rewrite in slope-intercept form.

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

$y = m x + b$

Reorder $10$ and $- 3 x$ .

$y = - 3 x + 10$

Use the slope-intercept form to find the slope and y-intercept.

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

$m = - 3$

$b = 10$

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

Slope: $- 3$

y-intercept: $(0, 10)$

Slope: $- 3$

y-intercept: $(0, 10)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Reorder $10$ and $- 3 x$ .

$y = - 3 x + 10$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & 10 \\ 1 & 7 \end{array}$

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

Slope: $- 3$

y-intercept: $(0, 10)$

$\begin{array}{c} x & y \\ 0 & 10 \\ 1 & 7 \end{array}$

Slope: $- 3$

y-intercept: $(0, 10)$

$\begin{array}{c} x & y \\ 0 & 10 \\ 1 & 7 \end{array}$

Step 2

Graph $4 x - 4 y = 8$ .

Solve for $y$ .

Subtract $4 x$ from both sides of the equation.

$- 4 y = 8 - 4 x$

Divide each term in $- 4 y = 8 - 4 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 8 - 4 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- 4 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- 4 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{8}{- 4} + \frac{- 4 x}{- 4}$

Simplify the right side.

Simplify each term.

Divide $8$ by $- 4$ .

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

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

$y = - 2 + x$

Rewrite in slope-intercept form.

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

$y = m x + b$

Reorder $- 2$ and $x$ .

$y = x - 2$

Use the slope-intercept form to find the slope and y-intercept.

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

$m = 1$

$b = - 2$

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

Slope: $1$

y-intercept: $(0, - 2)$

Slope: $1$

y-intercept: $(0, - 2)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

Reorder $- 2$ and $x$ .

$y = x - 2$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & - 2 \\ 1 & - 1 \end{array}$

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

Slope: $1$

y-intercept: $(0, - 2)$

$\begin{array}{c} x & y \\ 0 & - 2 \\ 1 & - 1 \end{array}$

Slope: $1$

y-intercept: $(0, - 2)$

$\begin{array}{c} x & y \\ 0 & - 2 \\ 1 & - 1 \end{array}$

Step 3

Plot each graph on the same coordinate system.

$- 3 x - y = - 10$

$4 x - 4 y = 8$

Step 4

Graph -3x-y=-10 4x-4y=8

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