Find the Slope and y-intercept (0,32) , (100,212)

$(0, 32)$ , $(100, 212)$

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.

$m = \frac{212 - (32)}{100 - (0)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $32$ .

$m = \frac{212 - 32}{100 - (0)}$

Subtract $32$ from $212$ .

$m = \frac{180}{100 - (0)}$

Simplify the denominator.

Multiply $- 1$ by $0$ .

$m = \frac{180}{100 + 0}$

Add $100$ and $0$ .

$m = \frac{180}{100}$

Cancel the common factor of $180$ and $100$ .

Factor $20$ out of $180$ .

$m = \frac{20 (9)}{100}$

Cancel the common factors.

Factor $20$ out of $100$ .

$m = \frac{20 \cdot 9}{20 \cdot 5}$

Cancel the common factor.

$m = \frac{20 \cdot 9}{20 \cdot 5}$

Rewrite the expression.

$m = \frac{9}{5}$

Step 2

Find the value of the y-intercept.

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

$y = (\frac{9}{5}) x + b$

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

$y = (\frac{9}{5}) \cdot (0) + b$

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

$32 = (\frac{9}{5}) \cdot (0) + b$

Rewrite the equation as $(\frac{9}{5}) \cdot (0) + b = 32$ .

$(\frac{9}{5}) \cdot (0) + b = 32$

Simplify $(\frac{9}{5}) \cdot (0) + b$ .

Multiply $\frac{9}{5}$ by $0$ .

$0 + b = 32$

Add $0$ and $b$ .

$b = 32$

Step 3

List the slope and y-intercept.

Slope: $\frac{9}{5}$

y-intercept: $(0, 32)$

Step 4

Find the Slope and y-intercept (0,32) , (100,212)

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