Find the Slope and y-intercept (0,5) , (1,3)

$(0, 5)$ , $(1, 3)$

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.

$m = \frac{3 - (5)}{1 - (0)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $5$ .

$m = \frac{3 - 5}{1 - (0)}$

Subtract $5$ from $3$ .

$m = \frac{- 2}{1 - (0)}$

Simplify the denominator.

Multiply $- 1$ by $0$ .

$m = \frac{- 2}{1 + 0}$

Add $1$ and $0$ .

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

Divide $- 2$ by $1$ .

$m = - 2$

Find the value of the y-intercept.

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

$y = (- 2) \cdot x + b$

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

$y = (- 2) \cdot (0) + b$

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

$5 = (- 2) \cdot (0) + b$

Rewrite the equation as $(- 2) \cdot (0) + b = 5$ .

$(- 2) \cdot (0) + b = 5$

Simplify $(- 2) \cdot (0) + b$ .

Multiply $- 2$ by $0$ .

$0 + b = 5$

Add $0$ and $b$ .

$b = 5$

List the slope and y-intercept.

Slope: $- 2$

y-intercept: $(0, 5)$

Find the Slope and y-intercept (0,5) , (1,3)

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