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 =

Answer 1

Lines AB and CD are parallel. Using the given coordinates

The equation of line CD is $y=-\frac{1}{4}x+7$

Given :

Lines AB and CD are parallel. The coordinates of point A are (-2,5), the coordinates of point B are (6,3),the coordinates of point D are (8,5)

When two lines are parallel then their slopes are equal

Lets find the slope of AB using the given points

A is (-2,5)  and B is (6,3)

Find slope using slope formula

$slope m =\frac{y_2-y_1}{x_2-x_1} =\frac{3-5}{6+2} =-\frac{1}{4}$

Slope of AB is $-\frac{1}{4}$

Slope of AB  and CD  are same

Slope of CD is $-\frac{1}{4}$

Now we find equation of line CD y=mx+b

Use point slope formula

$y-y_1=m(x-x_1)$

use the given point D(8,5) and slope m

Substitute the values

$y-5=-\frac{1}{4} (x-8)\\\\y-5=-\frac{1}{4}x+2\\y=-\frac{1}{4}x+2+5\\y=-\frac{1}{4}x+7$

The equation of line CD is $y=-\frac{1}{4}x+7$

Learn more : brainly.com/question/17301100