$\text { Write an equation of the line that passes through the point } \left( \frac { 5 } { 4 } , \frac { 5 } { 8 } \right) \text { and is parallel to }$ the line $7 x - 3 y = 0$.
A) $56 x - 24 y - 55 = 0$
B) $56 x + 12 y - 55 = 0$
C) $56 x - 8 y + 55 = 0$
D) $56 x + 6 y + 55 = 0$
E) $56 x + 4 y - 55 = 0$

Question

Quizplus · Accepted Answer

To find the equation of a line parallel to $7x - 3y = 0$ and passing through $\left(\frac{5}{4}, \frac{5}{8}\right)$, first, find the slope of the given line by rewriting it in slope-intercept form $y = mx + b$. The given equation $7x - 3y = 0$ can be rewritten as $y = \frac{7}{3}x$, indicating a slope $m = \frac{7}{3}$. A line parallel to this will have the same slope. Using the point-slope form $y - y_1 = m(x - x_1)$ with $m = \frac{7}{3}$ and $(x_1, y_1) = \left(\frac{5}{4}, \frac{5}{8}\right)$, we get $y - \frac{5}{8} = \frac{7}{3}\left(x - \frac{5}{4}\right)$. Multiplying through to clear fractions and rearranging to the standard form $Ax + By = C$ leads to $56x - 24y - 55 = 0$.

The Line 7x−3y=07 x - 3 y = 07x−3y=0 A)

The Line $7 x - 3 y = 0$
A)