Question

11 multiple choice 5 points
find the equation of a line parallel to $y = 3x + 8$ that passes through the point $(5,6)$.
$y = -3x - 9$
$y = 3x - 9$
$-x - 3y = -23$
$-3x - y = -21$

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For $y=3x+8$, the slope $m=3$.

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $m=3$, $x_1=5$, $y_1=6$:
$y-6=3(x-5)$

Step3: Simplify to slope-intercept form

Expand and rearrange:
$y-6=3x-15$
$y=3x-15+6$
$y=3x-9$

Step4: Verify other options (optional)

• $y=-3x-9$ has slope $-3$ (not parallel)
• $-x-3y=-23$ rearranges to $y=-\frac{1}{3}x+\frac{23}{3}$ (slope $-\frac{1}{3}$, not parallel)
• $-3x-y=-21$ rearranges to $y=-3x+21$ (slope $-3$, not parallel)

Answer:

y = 3x - 9