Write an equation for the line described. Write the equation in the form specified.
-parallel to $y + 6 x = 4$, through $( 4,5 )$; slope-intercept form
A) $y = - 6 x - 29$
B) $y = - \frac { 1 } { 6 } x - \frac { 29 } { 6 }$
C) $y = 6 x - 29$
D) $y = - 6 x + 29$

Question

Quizplus · Accepted Answer

Parallel lines have the same slope. The given equation $y + 6x = 4$ can be rewritten in slope-intercept form as $y = -6x + 4$, indicating a slope of $-6$. For a line parallel to this through $(4,5)$, we use the slope $-6$ and the point to find the y-intercept using $y = mx + b$, where $m = -6$, $x = 4$, and $y = 5$. Solving for $b$, we get $5 = -6(4) + b$, leading to $b = 29$. Thus, the equation is $y = -6x + 29$.

Write an Equation for the Line Described y+6x=4y + 6 x = 4y+6x=4

Write an Equation for the Line Described $y + 6 x = 4$