Question

3
select the correct answer from each drop - down menu.
consider the given equation.
$3x + 2y = 8$
the equation $y = \square x + \square$ represents the line parallel to the given equation and passes through the point $(-2,5)$.
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Explanation:

Step1: Rewrite given equation to slope-intercept

$$3x + 2y = 8 \implies 2y = -3x + 8 \implies y = -\frac{3}{2}x + 4$$

Step2: Identify parallel line slope

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

Step3: Substitute point to find intercept

Use point $(-2,5)$ in $y = mx + b$:
$$5 = -\frac{3}{2}(-2) + b \implies 5 = 3 + b$$

Step4: Solve for intercept $b$

$$b = 5 - 3 = 2$$

Answer:

The equation is $y = -\frac{3}{2}x + 2$, so the first blank is $\boldsymbol{-\frac{3}{2}}$ and the second blank is $\boldsymbol{2}$.