Question

question find the equation of a line parallel to $-4y = 32 - 6x$ that passes through the point $(2, 8)$. answer $y = \frac{3}{2}x + 5$ $y = -\frac{3}{2}x + 5$ $4x + 6y = 56$ $6x + 4y = 44$ submit answer

Explanation:

Step1: Convert to slope-intercept form

Rearrange $-4y = 32 - 6x$ to $y=mx+b$:

$$\begin{align*} -4y &= -6x + 32 \\ y &= \frac{-6}{-4}x + \frac{32}{-4} \\ y &= \frac{3}{2}x - 8 \end{align*}$$

Step2: Identify parallel slope

Parallel lines have equal slopes, so $m=\frac{3}{2}$.

Step3: Use point-slope form

Use point $(2,8)$ and $y-y_1=m(x-x_1)$:

$$ y - 8 = \frac{3}{2}(x - 2) $$

Step4: Simplify to slope-intercept

Expand and isolate $y$:

$$\begin{align*} y - 8 &= \frac{3}{2}x - 3 \\ y &= \frac{3}{2}x + 5 \end{align*}$$

Step5: Verify other options (optional)

Check if $4x+6y=56$ simplifies to match:

$$\begin{align*} 6y &= -4x + 56 \\ y &= -\frac{2}{3}x + \frac{28}{3} \end{align*}$$

Slope does not match. For $6x+4y=44$:

$$\begin{align*} 4y &= -6x + 44 \\ y &= -\frac{3}{2}x + 11 \end{align*}$$

Slope does not match. $y=-\frac{3}{2}x+5$ has opposite slope, not parallel.

Answer:

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