Find the Slope and y-intercept (1,5) , (-2,14)

$(1, 5)$ , $(- 2, 14)$

Step 1

Find the value of the slope.

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.

$m = \frac{14 - (5)}{- 2 - (1)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $5$ .

$m = \frac{14 - 5}{- 2 - (1)}$

Subtract $5$ from $14$ .

$m = \frac{9}{- 2 - (1)}$

Simplify the denominator.

Multiply $- 1$ by $1$ .

$m = \frac{9}{- 2 - 1}$

Subtract $1$ from $- 2$ .

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

Divide $9$ by $- 3$ .

$m = - 3$

Step 2

Find the value of the y-intercept.

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

$y = (- 3) \cdot x + b$

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

$y = (- 3) \cdot (1) + b$

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

$5 = (- 3) \cdot (1) + b$

Rewrite the equation as $(- 3) \cdot (1) + b = 5$ .

$(- 3) \cdot (1) + b = 5$

Multiply $- 3$ by $1$ .

$- 3 + b = 5$

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

Add $3$ to both sides of the equation.

$b = 5 + 3$

Add $5$ and $3$ .

$b = 8$

Step 3

List the slope and y-intercept.

Slope: $- 3$

y-intercept: $(0, 8)$

Step 4

Find the Slope and y-intercept (1,5) , (-2,14)

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