Find the Slope and Y-Intercept (-19,16) , (-10,19)

$(- 19, 16)$ , $(- 10, 19)$

Find the value of the slope.

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

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

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).

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

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

$m = \frac{19 - (16)}{- 10 - (- 19)}$

Simplify.

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Simplify the numerator.

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Multiply $- 1$ by $16$ .

$m = \frac{19 - 16}{- 10 - (- 19)}$

Subtract $16$ from $19$ .

$m = \frac{3}{- 10 - (- 19)}$

Simplify the denominator.

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Multiply $- 1$ by $- 19$ .

$m = \frac{3}{- 10 + 19}$

Add $- 10$ and $19$ .

$m = \frac{3}{9}$

Cancel the common factor of $3$ and $9$ .

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Factor $3$ out of $3$ .

$m = \frac{3 (1)}{9}$

Cancel the common factors.

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Factor $3$ out of $9$ .

$m = \frac{3 \cdot 1}{3 \cdot 3}$

Cancel the common factor.

$m = \frac{3 \cdot 1}{3 \cdot 3}$

Rewrite the expression.

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

Find the value of the y-intercept.

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

$y = (\frac{1}{3}) x + b$

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

$y = (\frac{1}{3}) \cdot (- 19) + b$

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

$16 = (\frac{1}{3}) \cdot (- 19) + b$

Rewrite the equation as $(\frac{1}{3}) \cdot (- 19) + b = 16$ .

$(\frac{1}{3}) \cdot (- 19) + b = 16$

Simplify each term.

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Combine $\frac{1}{3}$ and $- 19$ .

$\frac{- 19}{3} + b = 16$

Move the negative in front of the fraction.

$- \frac{19}{3} + b = 16$

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

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Add $\frac{19}{3}$ to both sides of the equation.

$b = 16 + \frac{19}{3}$

To write $16$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = 16 \cdot \frac{3}{3} + \frac{19}{3}$

Combine $16$ and $\frac{3}{3}$ .

$b = \frac{16 \cdot 3}{3} + \frac{19}{3}$

Combine the numerators over the common denominator.

$b = \frac{16 \cdot 3 + 19}{3}$

Simplify the numerator.

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Multiply $16$ by $3$ .

$b = \frac{48 + 19}{3}$

Add $48$ and $19$ .

$b = \frac{67}{3}$

The values of the slope and y-intercept are $m = \frac{1}{3}$ and $b = \frac{67}{3}$ .

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

$b = \frac{67}{3}$

Find the Slope and Y-Intercept (-19,16) , (-10,19)

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