Question

consider the following equation.
$8y - 10 = -3(4 - 2x)$
step 2 of 2: find the equation of the line which passes through the point $(10, 7)$ and is parallel to the given line. express your answer in slope - intercept form. simplify your answer.
answer 2 points
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Explanation:

Step1: Simplify given line to slope-intercept form

Start with the given equation:
$8y - 10 = -3(4 - 2x)$
Expand the right-hand side:
$8y - 10 = -12 + 6x$
Add 10 to both sides:
$8y = 6x - 2$
Divide all terms by 8:
$y = \frac{6}{8}x - \frac{2}{8}$
Simplify the fractions:
$y = \frac{3}{4}x - \frac{1}{4}$

Step2: Identify slope of parallel line

Parallel lines have equal slopes. From Step1, the slope $m = \frac{3}{4}$.

Step3: Use point-slope form to find new line

Use the point $(10, 7)$ and slope $\frac{3}{4}$ in the point-slope formula $y - y_1 = m(x - x_1)$:
$y - 7 = \frac{3}{4}(x - 10)$

Step4: Convert to slope-intercept form

Expand the right-hand side:
$y - 7 = \frac{3}{4}x - \frac{30}{4}$
Simplify $\frac{30}{4}$ to $\frac{15}{2}$, then add 7 (which is $\frac{14}{2}$) to both sides:
$y = \frac{3}{4}x - \frac{15}{2} + \frac{14}{2}$
Combine the constant terms:
$y = \frac{3}{4}x - \frac{1}{2}$

Answer:

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