Find the Slope and y-intercept (0,0) ; (3,4)

$(0, 0)$ ; $(3, 4)$

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.

$m = \frac{4 - (0)}{3 - (0)}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $0$ .

$m = \frac{4 + 0}{3 - (0)}$

Add $4$ and $0$ .

$m = \frac{4}{3 - (0)}$

Simplify the denominator.

Multiply $- 1$ by $0$ .

$m = \frac{4}{3 + 0}$

Add $3$ and $0$ .

$m = \frac{4}{3}$

Step 2

Find the value of the y-intercept.

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

$y = (\frac{4}{3}) x + b$

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

$y = (\frac{4}{3}) \cdot (0) + b$

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

$0 = (\frac{4}{3}) \cdot (0) + b$

Rewrite the equation as $(\frac{4}{3}) \cdot (0) + b = 0$ .

$(\frac{4}{3}) \cdot (0) + b = 0$

Simplify $(\frac{4}{3}) \cdot (0) + b$ .

Multiply $\frac{4}{3}$ by $0$ .

$0 + b = 0$

Add $0$ and $b$ .

$b = 0$

Step 3

List the slope and y-intercept.

Slope: $\frac{4}{3}$

y-intercept: $(0, 0)$

Step 4

Find the Slope and y-intercept (0,0) ; (3,4)

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