Find the Slope and y-intercept (5,10) , (7,14)

$(5, 10)$ , $(7, 14)$

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.

$m = \frac{14 - (10)}{7 - (5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $10$ .

$m = \frac{14 - 10}{7 - (5)}$

Subtract $10$ from $14$ .

$m = \frac{4}{7 - (5)}$

Simplify the denominator.

Multiply $- 1$ by $5$ .

$m = \frac{4}{7 - 5}$

Subtract $5$ from $7$ .

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

Divide $4$ by $2$ .

$m = 2$

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, $y = m x + b$ .

$y = (2) \cdot (5) + b$

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

$10 = (2) \cdot (5) + b$

Rewrite the equation as $(2) \cdot (5) + b = 10$ .

$(2) \cdot (5) + b = 10$

Multiply $2$ by $5$ .

$10 + b = 10$

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

Subtract $10$ from both sides of the equation.

$b = 10 - 10$

Subtract $10$ from $10$ .

$b = 0$

List the slope and y-intercept.

Slope: $2$

y-intercept: $(0, 0)$

Find the Slope and y-intercept (5,10) , (7,14)

Related Questions

Support LCMGCF.com by disabling your adblocker.