Pre-Algebra Examples

$(3, 10)$ , $(- 14, - 4)$

Step 1

Find the value of the slope.

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Step 1.1

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

Step 1.2

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 1.3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 4 - (10)}{- 14 - (3)}$

Step 1.4

Simplify.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Multiply $- 1$ by $10$ .

$m = \frac{- 4 - 10}{- 14 - (3)}$

Step 1.4.1.2

Subtract $10$ from $- 4$ .

$m = \frac{- 14}{- 14 - (3)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $3$ .

$m = \frac{- 14}{- 14 - 3}$

Step 1.4.2.2

Subtract $3$ from $- 14$ .

$m = \frac{- 14}{- 17}$

Step 1.4.3

Dividing two negative values results in a positive value.

$m = \frac{14}{17}$

Step 2

Find the value of the y-intercept.

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Step 2.1

Substitute the value of $m$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (\frac{14}{17}) x + b$

Step 2.2

Substitute the value of $x$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (\frac{14}{17}) \cdot (3) + b$

Step 2.3

Substitute the value of $y$ into the slope-intercept form of the equation, $y = m x + b$ .

$10 = (\frac{14}{17}) \cdot (3) + b$

Step 2.4

Rewrite the equation as $(\frac{14}{17}) \cdot (3) + b = 10$ .

$(\frac{14}{17}) \cdot (3) + b = 10$

Step 2.5

Multiply $(\frac{14}{17}) (3)$ .

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Step 2.5.1

Combine $\frac{14}{17}$ and $3$ .

$\frac{14 \cdot 3}{17} + b = 10$

Step 2.5.2

Multiply $14$ by $3$ .

$\frac{42}{17} + b = 10$

Step 2.6

Move all terms not containing $b$ to the right side of the equation.

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Step 2.6.1

Subtract $\frac{42}{17}$ from both sides of the equation.

$b = 10 - \frac{42}{17}$

Step 2.6.2

To write $10$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$b = 10 \cdot \frac{17}{17} - \frac{42}{17}$

Step 2.6.3

Combine $10$ and $\frac{17}{17}$ .

$b = \frac{10 \cdot 17}{17} - \frac{42}{17}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{10 \cdot 17 - 42}{17}$

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $10$ by $17$ .

$b = \frac{170 - 42}{17}$

Step 2.6.5.2

Subtract $42$ from $170$ .

$b = \frac{128}{17}$

Step 3

List the slope and y-intercept.

Slope: $\frac{14}{17}$

y-intercept: $(0, \frac{128}{17})$

Step 4