Find the Slope and y-intercept (3,4) , (5,16)

$(3, 4)$ , $(5, 16)$

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.

$m = \frac{16 - (4)}{5 - (3)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $4$ .

$m = \frac{16 - 4}{5 - (3)}$

Subtract $4$ from $16$ .

$m = \frac{12}{5 - (3)}$

Simplify the denominator.

Multiply $- 1$ by $3$ .

$m = \frac{12}{5 - 3}$

Subtract $3$ from $5$ .

$m = \frac{12}{2}$

Divide $12$ by $2$ .

$m = 6$

Step 2

Find the value of the y-intercept.

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

$y = (6) \cdot x + b$

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

$y = (6) \cdot (3) + b$

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

$4 = (6) \cdot (3) + b$

Rewrite the equation as $(6) \cdot (3) + b = 4$ .

$(6) \cdot (3) + b = 4$

Multiply $6$ by $3$ .

$18 + b = 4$

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

Subtract $18$ from both sides of the equation.

$b = 4 - 18$

Subtract $18$ from $4$ .

$b = - 14$

Step 3

List the slope and y-intercept.

Slope: $6$

y-intercept: $(0, - 14)$

Step 4

Find the Slope and y-intercept (3,4) , (5,16)

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