Graph 3x+y=1 2x-y=-6

$3 x + y = 1$ $2 x - y = - 6$

Step 1

Graph $3 x + y = 1$ .

Subtract $3 x$ from both sides of the equation.

$y = 1 - 3 x$

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 $1$ and $- 3 x$ .

$y = - 3 x + 1$

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

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

$m = - 3$

$b = 1$

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

Slope: $- 3$

y-intercept: $(0, 1)$

Slope: $- 3$

y-intercept: $(0, 1)$

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 $1$ and $- 3 x$ .

$y = - 3 x + 1$

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

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

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

Slope: $- 3$

y-intercept: $(0, 1)$

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

Slope: $- 3$

y-intercept: $(0, 1)$

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

Step 2

Graph $2 x - y = - 6$ .

Solve for $y$ .

Subtract $2 x$ from both sides of the equation.

$- y = - 6 - 2 x$

Divide each term in $- y = - 6 - 2 x$ by $- 1$ and simplify.

Divide each term in $- y = - 6 - 2 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 6}{- 1} + \frac{- 2 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 6}{- 1} + \frac{- 2 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 6}{- 1} + \frac{- 2 x}{- 1}$

Simplify the right side.

Simplify each term.

Divide $- 6$ by $- 1$ .

$y = 6 + \frac{- 2 x}{- 1}$

Move the negative one from the denominator of $\frac{- 2 x}{- 1}$ .

$y = 6 - 1 \cdot (- 2 x)$

Rewrite $- 1 \cdot (- 2 x)$ as $- (- 2 x)$ .

$y = 6 - (- 2 x)$

Multiply $- 2$ by $- 1$ .

$y = 6 + 2 x$

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 $6$ and $2 x$ .

$y = 2 x + 6$

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

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

$m = 2$

$b = 6$

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

Slope: $2$

y-intercept: $(0, 6)$

Slope: $2$

y-intercept: $(0, 6)$

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 $6$ and $2 x$ .

$y = 2 x + 6$

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

$\begin{array}{c} x & y \\ 0 & 6 \\ 1 & 8 \end{array}$

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

Slope: $2$

y-intercept: $(0, 6)$

$\begin{array}{c} x & y \\ 0 & 6 \\ 1 & 8 \end{array}$

Slope: $2$

y-intercept: $(0, 6)$

$\begin{array}{c} x & y \\ 0 & 6 \\ 1 & 8 \end{array}$

Step 3

Plot each graph on the same coordinate system.

$3 x + y = 1$

$2 x - y = - 6$

Step 4

Graph 3x+y=1 2x-y=-6

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