Find the Equation Using Point-Slope Formula (-1/2,3) , (0,0)

$(- \frac{1}{2}, 3)$ , $(0, 0)$

Step 1

Find the slope of the line between $(- \frac{1}{2}, 3)$ and $(0, 0)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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.

$m = \frac{0 - (3)}{0 - (- \frac{1}{2})}$

Simplify.

Simplify the numerator.

Multiply $- 1$ by $3$ .

$m = \frac{0 - 3}{0 + \frac{1}{2}}$

Subtract $3$ from $0$ .

$m = \frac{- 3}{0 + \frac{1}{2}}$

Simplify the denominator.

Multiply $- - \frac{1}{2}$ .

Multiply $- 1$ by $- 1$ .

$m = \frac{- 3}{0 + 1 (\frac{1}{2})}$

Multiply $\frac{1}{2}$ by $1$ .

$m = \frac{- 3}{0 + \frac{1}{2}}$

Add $0$ and $\frac{1}{2}$ .

$m = \frac{- 3}{\frac{1}{2}}$

Multiply the numerator by the reciprocal of the denominator.

$m = - 3 \cdot 2$

Multiply $- 3$ by $2$ .

$m = - 6$

Step 2

Use the slope $- 6$ and a given point $(- \frac{1}{2}, 3)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (3) = - 6 \cdot (x - (- \frac{1}{2}))$

Step 3

Simplify the equation and keep it in point-slope form.

$y - 3 = - 6 \cdot (x + \frac{1}{2})$

Step 4

Solve for $y$ .

Simplify $- 6 \cdot (x + \frac{1}{2})$ .

Rewrite.

$y - 3 = 0 + 0 - 6 \cdot (x + \frac{1}{2})$

Simplify by adding zeros.

$y - 3 = - 6 \cdot (x + \frac{1}{2})$

Apply the distributive property.

$y - 3 = - 6 x - 6 (\frac{1}{2})$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

$y - 3 = - 6 x + 2 (- 3) \frac{1}{2}$

Cancel the common factor.

$y - 3 = - 6 x + 2 \cdot - 3 \frac{1}{2}$

Rewrite the expression.

$y - 3 = - 6 x - 3$

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

Add $3$ to both sides of the equation.

$y = - 6 x - 3 + 3$

Combine the opposite terms in $- 6 x - 3 + 3$ .

Add $- 3$ and $3$ .

$y = - 6 x + 0$

Add $- 6 x$ and $0$ .

$y = - 6 x$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = - 6 x$

Point-slope form:

$y - 3 = - 6 \cdot (x + \frac{1}{2})$

Step 6

Find the Equation Using Point-Slope Formula (-1/2,3) , (0,0)

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