Find the Slope and y-intercept (5,16) , (7,21)

$(5, 16)$ , $(7, 21)$

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.

$m = \frac{21 - (16)}{7 - (5)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $16$ .

$m = \frac{21 - 16}{7 - (5)}$

Subtract $16$ from $21$ .

$m = \frac{5}{7 - (5)}$

Simplify the denominator.

Multiply $- 1$ by $5$ .

$m = \frac{5}{7 - 5}$

Subtract $5$ from $7$ .

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

Step 2

Find the value of the y-intercept.

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

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

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

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

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

$16 = (\frac{5}{2}) \cdot (5) + b$

Rewrite the equation as $(\frac{5}{2}) \cdot (5) + b = 16$ .

$(\frac{5}{2}) \cdot (5) + b = 16$

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

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

$\frac{5 \cdot 5}{2} + b = 16$

Multiply $5$ by $5$ .

$\frac{25}{2} + b = 16$

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

Subtract $\frac{25}{2}$ from both sides of the equation.

$b = 16 - \frac{25}{2}$

To write $16$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = 16 \cdot \frac{2}{2} - \frac{25}{2}$

Combine $16$ and $\frac{2}{2}$ .

$b = \frac{16 \cdot 2}{2} - \frac{25}{2}$

Combine the numerators over the common denominator.

$b = \frac{16 \cdot 2 - 25}{2}$

Simplify the numerator.

Multiply $16$ by $2$ .

$b = \frac{32 - 25}{2}$

Subtract $25$ from $32$ .

$b = \frac{7}{2}$

Step 3

List the slope and y-intercept.

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

y-intercept: $(0, \frac{7}{2})$

Step 4

Find the Slope and y-intercept (5,16) , (7,21)

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