Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
-Through $( - 7,11 )$ parallel to $4 x - 3 y = - 49$
A) $y = \frac { 4 } { 3 } x + \frac { 61 } { 3 }$
B) $y = \frac { 3 } { 4 } x + \frac { 11 } { 4 }$
C) $y = - \frac { 4 } { 3 } x - \frac { 61 } { 3 }$
D) $y = - \frac { 7 } { 3 } x + \frac { 49 } { 3 }$

Question

Quizplus · Accepted Answer

Lines that are parallel have the same slope. The given equation $4x - 3y = -49$ can be rewritten in slope-intercept form as $y = \frac{4}{3}x + \frac{49}{3}$. The slope of this line is $\frac{4}{3}$, so the parallel line through $(-7, 11)$ will also have a slope of $\frac{4}{3}$. Using the point-slope form $y - y_1 = m(x - x_1)$ with $m = \frac{4}{3}$, $x_1 = -7$, and $y_1 = 11$, we get $y - 11 = \frac{4}{3}(x + 7)$. Simplifying this to slope-intercept form gives $y = \frac{4}{3}x + \frac{61}{3}$.

Determine the Equation of the Line Described (−7,11)( - 7,11 )(−7,11)

Determine the Equation of the Line Described $( - 7,11 )$