Find the Slope and y-intercept (2,4) , (-3,7)

$(2, 4)$ , $(- 3, 7)$

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.

$m = \frac{7 - (4)}{- 3 - (2)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $4$ .

$m = \frac{7 - 4}{- 3 - (2)}$

Subtract $4$ from $7$ .

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

Simplify the denominator.

Multiply $- 1$ by $2$ .

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

Subtract $2$ from $- 3$ .

$m = \frac{3}{- 5}$

Move the negative in front of the fraction.

$m = - \frac{3}{5}$

Step 2

Find the value of the y-intercept.

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

$y = (- \frac{3}{5}) \cdot x + b$

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

$y = (- \frac{3}{5}) \cdot (2) + b$

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

$4 = (- \frac{3}{5}) \cdot (2) + b$

Rewrite the equation as $(- \frac{3}{5}) \cdot (2) + b = 4$ .

$(- \frac{3}{5}) \cdot (2) + b = 4$

Simplify each term.

Multiply $(- \frac{3}{5}) (2)$ .

Multiply $2$ by $- 1$ .

$- 2 (\frac{3}{5}) + b = 4$

Combine $- 2$ and $\frac{3}{5}$ .

$\frac{- 2 \cdot 3}{5} + b = 4$

Multiply $- 2$ by $3$ .

$\frac{- 6}{5} + b = 4$

Move the negative in front of the fraction.

$- \frac{6}{5} + b = 4$

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

Add $\frac{6}{5}$ to both sides of the equation.

$b = 4 + \frac{6}{5}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = 4 \cdot \frac{5}{5} + \frac{6}{5}$

Combine $4$ and $\frac{5}{5}$ .

$b = \frac{4 \cdot 5}{5} + \frac{6}{5}$

Combine the numerators over the common denominator.

$b = \frac{4 \cdot 5 + 6}{5}$

Simplify the numerator.

Multiply $4$ by $5$ .

$b = \frac{20 + 6}{5}$

Add $20$ and $6$ .

$b = \frac{26}{5}$

Step 3

List the slope and y-intercept.

Slope: $- \frac{3}{5}$

y-intercept: $(0, \frac{26}{5})$

Step 4

Find the Slope and y-intercept (2,4) , (-3,7)

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