Answer :
Answer:
[tex]y=-\dfrac{1}{4}x+5[/tex]
Step-by-step explanation:
Parallel Lines
When two linear equations are parallel to each other they always have the same slope and have different y-intercepts.
Finding the Equation of a Line
Their slopes can be calculated by taking two points from one respective line and plugging them into the slope formula,
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex],
where the subscripts 1 and 2 indicate from which coordinate pair the values originate from.
After finding their slopes, their b values can be found.
To find their respective y-intercepts, simply plug in one of their coordinate points and rearrange to find the value of b.
Solving the Problem
We're given two points from line AB and one from CD, so its best to use the points from AB to find CD's slope.
Let [tex](-2,5)=(x_2,y_2)[/tex] and [tex](6,3)=(x_1,y_1)[/tex],
[tex]\dfrac{5-3}{-2-6}=\dfrac{2}{-8} =-\dfrac{1}{4}[/tex].
So, the equation CD is currently
[tex]CD: y=-\dfrac{1}{4}x+b[/tex]
Now, let's find the y-intercept of line CD.
Plugging in its only coordinate point (8, 5),
[tex]5=-\dfrac{1}{4}(8)+b\\\\3= -2+b\\\\3+2=\boxed{5=b}[/tex].
Line CD's complete equation is,
[tex]CD: y=-\dfrac{1}{4}x+5[/tex].
