Graph -3x+2y=1

$- 3 x + 2 y = 1$

Step 1

Solve for $y$ .

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

$2 y = 1 + 3 x$

Divide each term in $2 y = 1 + 3 x$ by $2$ and simplify.

Divide each term in $2 y = 1 + 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{1}{2} + \frac{3 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{1}{2} + \frac{3 x}{2}$

Divide $y$ by $1$ .

$y = \frac{1}{2} + \frac{3 x}{2}$

Step 2

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 $\frac{1}{2}$ and $\frac{3 x}{2}$ .

$y = \frac{3 x}{2} + \frac{1}{2}$

Reorder terms.

$y = \frac{3}{2} x + \frac{1}{2}$

Step 3

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

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

$m = \frac{3}{2}$

$b = \frac{1}{2}$

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

Slope: $\frac{3}{2}$

y-intercept: $(0, \frac{1}{2})$

Slope: $\frac{3}{2}$

y-intercept: $(0, \frac{1}{2})$

Step 4

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.

Reorder $\frac{1}{2}$ and $\frac{3 x}{2}$ .

$y = \frac{3 x}{2} + \frac{1}{2}$

Reorder terms.

$y = \frac{3}{2} x + \frac{1}{2}$

Find the x-intercept.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{3}{2} x + \frac{1}{2}$

Solve the equation.

Rewrite the equation as $\frac{3}{2} x + \frac{1}{2} = 0$ .

$\frac{3}{2} x + \frac{1}{2} = 0$

Combine $\frac{3}{2}$ and $x$ .

$\frac{3 x}{2} + \frac{1}{2} = 0$

Subtract $\frac{1}{2}$ from both sides of the equation.

$\frac{3 x}{2} = - \frac{1}{2}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 x = - 1$

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

x-intercept(s) in point form.

x-intercept(s): $(- \frac{1}{3}, 0)$

Find the y-intercept.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{3}{2} \cdot (0) + \frac{1}{2}$

Solve the equation.

Multiply $\frac{3}{2}$ by $0$ .

$y = \frac{3}{2} \cdot 0 + \frac{1}{2}$

Remove parentheses.

$y = \frac{3}{2} \cdot (0) + \frac{1}{2}$

Simplify $\frac{3}{2} \cdot (0) + \frac{1}{2}$ .

Multiply $\frac{3}{2}$ by $0$ .

$y = 0 + \frac{1}{2}$

Add $0$ and $\frac{1}{2}$ .

$y = \frac{1}{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{2})$

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

$\begin{array}{c} x & y \\ - \frac{1}{3} & 0 \\ 0 & \frac{1}{2} \end{array}$

Step 5

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

Slope: $\frac{3}{2}$

y-intercept: $(0, \frac{1}{2})$

$\begin{array}{c} x & y \\ - \frac{1}{3} & 0 \\ 0 & \frac{1}{2} \end{array}$

Step 6

Graph -3x+2y=1

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