Find the Slope and y-intercept (1,4) , (2,2)

$(1, 4)$ , $(2, 2)$

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.

$m = \frac{2 - (4)}{2 - (1)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $4$ .

$m = \frac{2 - 4}{2 - (1)}$

Subtract $4$ from $2$ .

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

Simplify the denominator.

Multiply $- 1$ by $1$ .

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

Subtract $1$ from $2$ .

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

Divide $- 2$ by $1$ .

$m = - 2$

Step 2

Find the value of the y-intercept.

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

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

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

$y = (- 2) \cdot (1) + b$

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

$4 = (- 2) \cdot (1) + b$

Rewrite the equation as $(- 2) \cdot (1) + b = 4$ .

$(- 2) \cdot (1) + b = 4$

Multiply $- 2$ by $1$ .

$- 2 + b = 4$

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

Add $2$ to both sides of the equation.

$b = 4 + 2$

Add $4$ and $2$ .

$b = 6$

Step 3

List the slope and y-intercept.

Slope: $- 2$

y-intercept: $(0, 6)$

Step 4

Find the Slope and y-intercept (1,4) , (2,2)

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