Find the Slope and y-intercept (2,1) , (6,4)

$(2, 1)$ , $(6, 4)$

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.

$m = \frac{4 - (1)}{6 - (2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $1$ .

$m = \frac{4 - 1}{6 - (2)}$

Subtract $1$ from $4$ .

$m = \frac{3}{6 - (2)}$

Simplify the denominator.

Multiply $- 1$ by $2$ .

$m = \frac{3}{6 - 2}$

Subtract $2$ from $6$ .

$m = \frac{3}{4}$

Step 2

Find the value of the y-intercept.

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

$y = (\frac{3}{4}) x + b$

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

$y = (\frac{3}{4}) \cdot (2) + b$

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

$1 = (\frac{3}{4}) \cdot (2) + b$

Rewrite the equation as $(\frac{3}{4}) \cdot (2) + b = 1$ .

$(\frac{3}{4}) \cdot (2) + b = 1$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3}{2 (2)} \cdot 2 + b = 1$

Cancel the common factor.

$\frac{3}{2 \cdot 2} \cdot 2 + b = 1$

Rewrite the expression.

$\frac{3}{2} + b = 1$

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

Subtract $\frac{3}{2}$ from both sides of the equation.

$b = 1 - \frac{3}{2}$

Write $1$ as a fraction with a common denominator.

$b = \frac{2}{2} - \frac{3}{2}$

Combine the numerators over the common denominator.

$b = \frac{2 - 3}{2}$

Subtract $3$ from $2$ .

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

Move the negative in front of the fraction.

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

Step 3

List the slope and y-intercept.

Slope: $\frac{3}{4}$

y-intercept: $(0, - \frac{1}{2})$

Step 4

Find the Slope and y-intercept (2,1) , (6,4)

Related Questions

Support LCMGCF.com by disabling your adblocker.