Find the Slope and y-intercept (7,0) , (0,10)

$(7, 0)$ , $(0, 10)$

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.

$m = \frac{10 - (0)}{0 - (7)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{10 + 0}{0 - (7)}$

Add $10$ and $0$ .

$m = \frac{10}{0 - (7)}$

Simplify the denominator.

Multiply $- 1$ by $7$ .

$m = \frac{10}{0 - 7}$

Subtract $7$ from $0$ .

$m = \frac{10}{- 7}$

Move the negative in front of the fraction.

$m = - \frac{10}{7}$

Find the value of the y-intercept.

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

$y = (- \frac{10}{7}) \cdot x + b$

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

$y = (- \frac{10}{7}) \cdot (7) + b$

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

$0 = (- \frac{10}{7}) \cdot (7) + b$

Rewrite the equation as $(- \frac{10}{7}) \cdot (7) + b = 0$ .

$(- \frac{10}{7}) \cdot (7) + b = 0$

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{10}{7}$ into the numerator.

$\frac{- 10}{7} \cdot 7 + b = 0$

Cancel the common factor.

$\frac{- 10}{7} \cdot 7 + b = 0$

Rewrite the expression.

$- 10 + b = 0$

Add $10$ to both sides of the equation.

$b = 10$

List the slope and y-intercept.

Slope: $- \frac{10}{7}$

y-intercept: $(0, 10)$

Find the Slope and y-intercept (7,0) , (0,10)

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