Find the Slope and y-intercept (2,2) , (4,6)

$(2, 2)$ , $(4, 6)$

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.

$m = \frac{6 - (2)}{4 - (2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $2$ .

$m = \frac{6 - 2}{4 - (2)}$

Subtract $2$ from $6$ .

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

Simplify the denominator.

Multiply $- 1$ by $2$ .

$m = \frac{4}{4 - 2}$

Subtract $2$ from $4$ .

$m = \frac{4}{2}$

Divide $4$ by $2$ .

$m = 2$

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, $y = m x + b$ .

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

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

$2 = (2) \cdot (2) + b$

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

$(2) \cdot (2) + b = 2$

Multiply $2$ by $2$ .

$4 + b = 2$

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

Subtract $4$ from both sides of the equation.

$b = 2 - 4$

Subtract $4$ from $2$ .

$b = - 2$

Step 3

List the slope and y-intercept.

Slope: $2$

y-intercept: $(0, - 2)$

Step 4

Find the Slope and y-intercept (2,2) , (4,6)

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