Find the Parallel Line What is an equation of the line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6 ?

What is an equation of the line that passes through the point $(- 2, - 4)$ and is parallel to the line $5 x - 2 y = 6$ ?

Write the problem as a mathematical expression.

$(- 2, - 4)$ , $5 x - 2 y = 6$

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.

$y = m x + b$

Subtract $5 x$ from both sides of the equation.

$- 2 y = 6 - 5 x$

Divide each term in $- 2 y = 6 - 5 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 6 - 5 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{6}{- 2} + \frac{- 5 x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{6}{- 2} + \frac{- 5 x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{6}{- 2} + \frac{- 5 x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 2$ .

$y = - 3 + \frac{- 5 x}{- 2}$

Dividing two negative values results in a positive value.

$y = - 3 + \frac{5 x}{2}$

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

Reorder $- 3$ and $\frac{5 x}{2}$ .

$y = \frac{5 x}{2} - 3$

Reorder terms.

$y = \frac{5}{2} x - 3$

Using the slope-intercept form, the slope is $\frac{5}{2}$ .

$m = \frac{5}{2}$

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

Use the slope $\frac{5}{2}$ and a given point $(- 2, - 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 4) = \frac{5}{2} \cdot (x - (- 2))$

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

$y + 4 = \frac{5}{2} \cdot (x + 2)$

Solve for $y$ .

Simplify $\frac{5}{2} \cdot (x + 2)$ .

Rewrite.

$y + 4 = 0 + 0 + \frac{5}{2} \cdot (x + 2)$

Simplify by adding zeros.

$y + 4 = \frac{5}{2} \cdot (x + 2)$

Apply the distributive property.

$y + 4 = \frac{5}{2} x + \frac{5}{2} \cdot 2$

Combine $\frac{5}{2}$ and $x$ .

$y + 4 = \frac{5 x}{2} + \frac{5}{2} \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$y + 4 = \frac{5 x}{2} + \frac{5}{2} \cdot 2$

Rewrite the expression.

$y + 4 = \frac{5 x}{2} + 5$

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

Subtract $4$ from both sides of the equation.

$y = \frac{5 x}{2} + 5 - 4$

Subtract $4$ from $5$ .

$y = \frac{5 x}{2} + 1$

Reorder terms.

$y = \frac{5}{2} x + 1$

Find the Parallel Line What is an equation of the line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6 ?

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