Question

if two lines are parallel and the first has the equation $y=-(5)/(2)x + 9$, what is the equation of a parallel line passing through $(4,-1)$?

$\bigcirc$ $y=(5)/(2)x + 9$

$\bigcirc$ $y=-(5)/(2)x + 9$

$\bigcirc$ $y=-(5)/(2)x - 1$

$\bigcirc$ $y=(2)/(5)x - 1$

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. The given line is $y=-\frac{5}{2}x+9$, so the slope $m=-\frac{5}{2}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=-\frac{5}{2}$, $x_1=4$, $y_1=-1$.
$y - (-1) = -\frac{5}{2}(x - 4)$

Step3: Simplify to slope-intercept form

Simplify the equation:
$y + 1 = -\frac{5}{2}x + 10$
$y = -\frac{5}{2}x + 10 - 1$
$y = -\frac{5}{2}x + 9$

Answer:

B. $y=-(5)/(2)x+9$