Question

question
find the equation of a line parallel to $2y = 14 - 3x$ that passes through the point $(-4,5)$.
answer
$\bigcirc y = -\frac{2}{3}x + 7$
$\bigcirc y = \frac{2}{3}x + 7$
$\bigcirc y = \frac{3}{2}x - 1$
$\bigcirc y = -\frac{3}{2}x - 1$
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Explanation:

Step1: Convert to slope-intercept form

Start with the given line:
$$2y = 14 - 3x$$
Divide by 2:
$$y = -\frac{3}{2}x + 7$$

Step2: Identify parallel slope

Parallel lines have equal slopes, so the slope of the desired line is $m = -\frac{3}{2}$.

Step3: Use point-slope formula

Use point $(-4,5)$ and $m = -\frac{3}{2}$:
$$y - 5 = -\frac{3}{2}(x + 4)$$

Step4: Simplify to slope-intercept form

Expand and solve for $y$:
$$y - 5 = -\frac{3}{2}x - 6$$
$$y = -\frac{3}{2}x - 6 + 5$$
$$y = -\frac{3}{2}x - 1$$

Answer:

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