Find the Slope and y-intercept (2,-1) , (0,4)

$(2, - 1)$ , $(0, 4)$

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.

$m = \frac{4 - (- 1)}{0 - (2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $- 1$ .

$m = \frac{4 + 1}{0 - (2)}$

Add $4$ and $1$ .

$m = \frac{5}{0 - (2)}$

Simplify the denominator.

Multiply $- 1$ by $2$ .

$m = \frac{5}{0 - 2}$

Subtract $2$ from $0$ .

$m = \frac{5}{- 2}$

Move the negative in front of the fraction.

$m = - \frac{5}{2}$

Step 2

Find the value of the y-intercept.

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

$y = (- \frac{5}{2}) \cdot x + b$

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

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

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

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

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

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$- 5 + b = - 1$

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

Add $5$ to both sides of the equation.

$b = - 1 + 5$

Add $- 1$ and $5$ .

$b = 4$

Step 3

List the slope and y-intercept.

Slope: $- \frac{5}{2}$

y-intercept: $(0, 4)$

Step 4

Find the Slope and y-intercept (2,-1) , (0,4)

Related Questions

Support LCMGCF.com by disabling your adblocker.