Algebra Examples

$5 x - 2 y = 7$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Subtract $5 x$ from both sides of the equation.

$- 2 y = 7 - 5 x$

Step 1.3

Divide each term in $- 2 y = 7 - 5 x$ by $- 2$ and simplify.

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Step 1.3.1

Divide each term in $- 2 y = 7 - 5 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{7}{- 2} + \frac{- 5 x}{- 2}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 2$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{7}{- 2} + \frac{- 5 x}{- 2}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{7}{- 2} + \frac{- 5 x}{- 2}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{7}{2} + \frac{- 5 x}{- 2}$

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{7}{2} + \frac{5 x}{2}$

Step 1.4

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

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Step 1.4.1

Reorder $- \frac{7}{2}$ and $\frac{5 x}{2}$ .

$y = \frac{5 x}{2} - \frac{7}{2}$

Step 1.4.2

Reorder terms.

$y = \frac{5}{2} x - \frac{7}{2}$

Step 2

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

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Step 2.1

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

$m = \frac{5}{2}$

$b = - \frac{7}{2}$

Step 2.2

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

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

y-intercept: $(0, - \frac{7}{2})$

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

y-intercept: $(0, - \frac{7}{2})$

Step 3