Lines AB and CD are parallel. Using the given coordinates
The equation of line CD is [tex]y=-\frac{1}{4}x+7[/tex]
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
[tex]slope m =\frac{y_2-y_1}{x_2-x_1} =\frac{3-5}{6+2} =-\frac{1}{4}[/tex]
Slope of AB is [tex]-\frac{1}{4}[/tex]
Slope of AB and CD are same
Slope of CD is [tex]-\frac{1}{4}[/tex]
Now we find equation of line CD y=mx+b
Use point slope formula
[tex]y-y_1=m(x-x_1)\\[/tex]
use the given point D(8,5) and slope m
Substitute the values
[tex]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[/tex]
The equation of line CD is [tex]y=-\frac{1}{4}x+7[/tex]
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