Find the Parallel Line through: (4,2) ; parallel to y=-3/4x-5

through: $(4, 2)$ ; parallel to $y = - \frac{3}{4} x - 5$

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.

Simplify each term.

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

$y = - \frac{x \cdot 3}{4} - 5$

Move $3$ to the left of $x$ .

$y = - \frac{3 x}{4} - 5$

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{3}{4} x) - 5$

Remove parentheses.

$y = - \frac{3}{4} x - 5$

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 $(4, 2)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

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

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

Solve for $y$ .

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

Rewrite.

$y - 2 = 0 + 0 - \frac{3}{4} \cdot (x - 4)$

Simplify terms.

Apply the distributive property.

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

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

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

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

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

Factor $4$ out of $- 4$ .

$y - 2 = - \frac{x \cdot 3}{4} + \frac{- 3}{4} \cdot (4 (- 1))$

Cancel the common factor.

$y - 2 = - \frac{x \cdot 3}{4} + \frac{- 3}{4} \cdot (4 \cdot - 1)$

Rewrite the expression.

$y - 2 = - \frac{x \cdot 3}{4} - 3 \cdot - 1$

Multiply $- 3$ by $- 1$ .

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

Move $3$ to the left of $x$ .

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

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

Add $2$ to both sides of the equation.

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

Add $3$ and $2$ .

$y = - \frac{3 x}{4} + 5$

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{3}{4} x) + 5$

Remove parentheses.

$y = - \frac{3}{4} x + 5$

Find the Parallel Line through: (4,2) ; parallel to y=-3/4x-5

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