Find the Parallel Line through: (-4,0) ; parallel to y=3/4x-2

through: $(- 4, 0)$ ; parallel to $y = \frac{3}{4} x - 2$

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Simplify the right side.

Combine $\frac{3}{4}$ and $x$ .

$y = \frac{3 x}{4} - 2$

Reorder terms.

$y = \frac{3}{4} x - 2$

Using the slope-intercept form, the slope is $\frac{3}{4}$ .

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

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope $\frac{3}{4}$ and a given point $(- 4, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = \frac{3}{4} \cdot (x - (- 4))$

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

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

Solve for $y$ .

Add $y$ and $0$ .

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

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

Apply the distributive property.

$y = \frac{3}{4} x + \frac{3}{4} \cdot 4$

Combine $\frac{3}{4}$ and $x$ .

$y = \frac{3 x}{4} + \frac{3}{4} \cdot 4$

Cancel the common factor of $4$ .

Cancel the common factor.

$y = \frac{3 x}{4} + \frac{3}{4} \cdot 4$

Rewrite the expression.

$y = \frac{3 x}{4} + 3$

Reorder terms.

$y = \frac{3}{4} x + 3$

Find the Parallel Line through: (-4,0) ; parallel to y=3/4x-2

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