Find an equation of the line. Write the equation using function notation.
-Through $( 3,2 )$; parallel to $9 x + 5 y = 17$
A) $f ( x ) = - \frac { 9 } { 5 } x + \frac { 37 } { 5 }$
B) $f ( x ) = - \frac { 5 } { 9 } x + 17$
C) $f ( x ) = - \frac { 5 } { 9 } x + 2$
D) $f ( x ) = \frac { 9 } { 5 } x + \frac { 37 } { 5 }$

Question

Quizplus · Accepted Answer

Lines that are parallel have the same slope. The given equation $9x + 5y = 17$ can be rewritten in slope-intercept form as $y = -\frac{9}{5}x + \frac{17}{5}$, indicating a slope of $-\frac{9}{5}$. To find the equation of a line parallel to this line and passing through $(3,2)$, we use the point-slope form $y - y_1 = m(x - x_1)$, where $m = -\frac{9}{5}$, $x_1 = 3$, and $y_1 = 2$. Simplifying this gives $y = -\frac{9}{5}x + \frac{37}{5}$, or in function notation, $f(x) = -\frac{9}{5}x + \frac{37}{5}$.

Find an Equation of the Line (3,2)( 3,2 )(3,2) ; Parallel To

Find an Equation of the Line $( 3,2 )$ ; Parallel To