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

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

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.

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

Simplify.

Simplify the numerator.

Multiply $- 1$ by $1$ .

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

Subtract $1$ from $- 4$ .

$m = \frac{- 5}{0 - (4)}$

Simplify the denominator.

Multiply $- 1$ by $4$ .

$m = \frac{- 5}{0 - 4}$

Subtract $4$ from $0$ .

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

Dividing two negative values results in a positive value.

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

Step 2

Find the value of the y-intercept.

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

$y = (\frac{5}{4}) x + b$

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

$y = (\frac{5}{4}) \cdot (4) + b$

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

$1 = (\frac{5}{4}) \cdot (4) + b$

Rewrite the equation as $(\frac{5}{4}) \cdot (4) + b = 1$ .

$(\frac{5}{4}) \cdot (4) + b = 1$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{5}{4} \cdot 4 + b = 1$

Rewrite the expression.

$5 + b = 1$

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

Subtract $5$ from both sides of the equation.

$b = 1 - 5$

Subtract $5$ from $1$ .

$b = - 4$

Step 3

List the slope and y-intercept.

Slope: $\frac{5}{4}$

y-intercept: $(0, - 4)$

Step 4

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

Related Questions

Support LCMGCF.com by disabling your adblocker.