Graph 3x-2y=5 - MathMaster

$3 x - 2 y = 5$

Solve for $y$ .

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

$- 2 y = 5 - 3 x$

Divide each term by $- 2$ and simplify.

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Divide each term in $- 2 y = 5 - 3 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{5}{- 2} + \frac{- 3 x}{- 2}$

Cancel the common factor of $- 2$ .

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Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{5}{- 2} + \frac{- 3 x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{5}{- 2} + \frac{- 3 x}{- 2}$

Simplify each term.

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Move the negative in front of the fraction.

$y = - \frac{5}{2} + \frac{- 3 x}{- 2}$

Dividing two negative values results in a positive value.

$y = - \frac{5}{2} + \frac{3 x}{2}$

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 $- \frac{5}{2}$ and $\frac{3 x}{2}$ .

$y = \frac{3 x}{2} - \frac{5}{2}$

Rewrite in slope-intercept form.

$y = \frac{3}{2} x - \frac{5}{2}$

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 $y = m x + b$ .

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

$b = - \frac{5}{2}$

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: $- \frac{5}{2}$

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

y-intercept: $- \frac{5}{2}$

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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Choose $1$ to substitute in for $x$ to find the ordered pair.

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Replace the variable $x$ with $1$ in the expression.

$f (1) = \frac{3 (1)}{2} - \frac{5}{2}$

Simplify the result.

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Multiply $3$ by $1$ .

$f (1) = \frac{3}{2} - \frac{5}{2}$

Combine the numerators over the common denominator.

$f (1) = \frac{3 - 5}{2}$

Subtract $5$ from $3$ .

$f (1) = \frac{- 2}{2}$

Divide $- 2$ by $2$ .

$f (1) = - 1$

The final answer is $- 1$ .

$- 1$

The $y$ value at $x = 1$ is $- 1$ .

$y = - 1$

Choose $3$ to substitute in for $x$ to find the ordered pair.

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Replace the variable $x$ with $3$ in the expression.

$f (3) = \frac{3 (3)}{2} - \frac{5}{2}$

Simplify the result.

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Multiply $3$ by $3$ .

$f (3) = \frac{9}{2} - \frac{5}{2}$

Combine the numerators over the common denominator.

$f (3) = \frac{9 - 5}{2}$

Subtract $5$ from $9$ .

$f (3) = \frac{4}{2}$

Divide $4$ by $2$ .

$f (3) = 2$

The final answer is $2$ .

$2$

The $y$ value at $x = 3$ is $2$ .

$y = 2$

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

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

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

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

y-intercept: $- \frac{5}{2}$

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

Graph 3x-2y=5

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