Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s)
lines ab and cd are parallel. the coordinates of point a are (-2,5), the coordinates of point b are (6,3), and the coordinates of point d are (8,5)
the equation of line cd is y = \boxed{} x + \boxed{}

Explanation:

Step1: Calculate slope of AB

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m_{AB} = \frac{3 - 5}{6 - (-2)} = \frac{-2}{8} = -\frac{1}{4}$

Step2: Slope of CD equals AB

Parallel lines have equal slopes, so $m_{CD} = -\frac{1}{4}$

Step3: Find y-intercept of CD

Use point D(8,5) in $y = mx + b$:
$5 = -\frac{1}{4}(8) + b$
$5 = -2 + b$
$b = 5 + 2 = 7$

Answer:

$y = -\frac{1}{4}x + 7$
The first box is $-\frac{1}{4}$ (or -1/4) and the second box is 7.