Find an equation for the line with the given properties.
-Passing through $( 4,4 )$ and parallel to the line whose equation is $2 x + y - 8 = 0$; slope-intercept form
A) $y = - 2 x + 12$
B) $y = 2 x - 12$
C) $y = - 2 x - 12$
D) $y = - \frac { 1 } { 2 } x - 6$

Question

Quizplus · Accepted Answer

Lines that are parallel have the same slope. The given line $2x + y - 8 = 0$ can be rewritten in slope-intercept form as $y = -2x + 8$, indicating a slope of $-2$. To find the equation of a line parallel to this line and passing through $(4,4)$, we use the slope $-2$ and the point to plug into the point-slope form equation $y - y_1 = m(x - x_1)$, which gives $y - 4 = -2(x - 4)$. Simplifying this, we get $y = -2x + 12$, which matches choice A.

Find an Equation for the Line with the Given Properties (4,4)( 4,4 )(4,4)

Find an Equation for the Line with the Given Properties $( 4,4 )$