Graph 3x-2y=1 - MathMaster

$3 x - 2 y = 1$

Solve for $y$ .

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

$- 2 y = 1 - 3 x$

Divide each term by $- 2$ and simplify.

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

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

Cancel the common factor of $- 2$ .

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify each term.

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Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

Rewrite in slope-intercept form.

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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.

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

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

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

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

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Find the x-intercept.

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

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

Solve the equation.

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

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

Add $\frac{1}{2}$ to 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 by $3$ and simplify.

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

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

Cancel the common factor of $3$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

x-intercept(s) in point form.

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

Find the y-intercept.

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

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

Solve the equation.

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Remove parentheses.

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

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

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Combine the numerators over the common denominator.

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

Simplify the expression.

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Multiply $3$ by $0$ .

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

Add $- 1$ and $0$ .

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

Move the negative in front of the fraction.

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

y-intercept(s) in point form.

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

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

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

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

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

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

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

Graph 3x-2y=1

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