Find the Slope and y-intercept (2,5) , (6,7)

$(2, 5)$ , $(6, 7)$

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.

$m = \frac{7 - (5)}{6 - (2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $5$ .

$m = \frac{7 - 5}{6 - (2)}$

Subtract $5$ from $7$ .

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

Simplify the denominator.

Multiply $- 1$ by $2$ .

$m = \frac{2}{6 - 2}$

Subtract $2$ from $6$ .

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

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Find the value of the y-intercept.

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

$y = (\frac{1}{2}) x + b$

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

$y = (\frac{1}{2}) \cdot (2) + b$

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

$5 = (\frac{1}{2}) \cdot (2) + b$

Rewrite the equation as $(\frac{1}{2}) \cdot (2) + b = 5$ .

$(\frac{1}{2}) \cdot (2) + b = 5$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{2} \cdot 2 + b = 5$

Rewrite the expression.

$1 + b = 5$

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

Subtract $1$ from both sides of the equation.

$b = 5 - 1$

Subtract $1$ from $5$ .

$b = 4$

Step 3

List the slope and y-intercept.

Slope: $\frac{1}{2}$

y-intercept: $(0, 4)$

Step 4

Find the Slope and y-intercept (2,5) , (6,7)

Related Questions

Support LCMGCF.com by disabling your adblocker.