Graph f(x,y)=1-3x+2y

$f (x, y) = 1 - 3 x + 2 y$

Rewrite the function as an equation.

$y = 1 - 3 x + 2 y$

Move all terms containing $y$ to the left side of the equation.

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

$y - 2 y = 1 - 3 x$

Subtract $2 y$ from $y$ .

$- y = 1 - 3 x$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $1$ by $- 1$ .

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

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

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

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

$y = - 1 - (- 3 x)$

Multiply $- 3$ by $- 1$ .

$y = - 1 + 3 x$

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.

Write in $y = m x + b$ form.

Solve for $y$ .

Move all terms containing $y$ to the left side of the equation.

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

$y - 2 y = 1 - 3 x$

Subtract $2 y$ from $y$ .

$- y = 1 - 3 x$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $1$ by $- 1$ .

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

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

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

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

$y = - 1 - (- 3 x)$

Multiply $- 3$ by $- 1$ .

$y = - 1 + 3 x$

Rearrange terms.

$y = 3 x - 1$

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: $(0, - 1)$

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

Graph f(x,y)=1-3x+2y

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