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19 votes
19 votes
The equation of line AB is y = 5x + 1. Write an equation of a line parallel to line AB in slope-intercept form that contains point (4, 5).Group of answer choicesy = (1/5)x − 29/ 5 y=(1/5)x+21/5y = 5x + 15y = 5x − 15

User Williamson
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2 Answers

10 votes
10 votes

Answer:

y= 5x - 15

Explanation:

:)

User Stephen Foster
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15 votes
15 votes

Given the equation of the line AB:


y=5x+1

You can identify that it is written in Slope-Intercept Form:


y=mx+b

Where "m" is the slope of the line and "b" is the y-intercept.

Notice that the slope of the line AB is:


m_(AB)=5

And its y-intercept is:


b_(AB)=1

By definition, parallel lines have the same slope but different y-intercepts. Therefore, you can determine that the slope of the line parallel to line AB is:


m=5

You know that it contains the point:


(4,5)

Therefore, you can substitute the slope and the coordinates of that point into this equation:


y=mx+b

And then solve for "b", in order to find the y-intercept:


5=(5)(4)+b
\begin{gathered} 5-20=b \\ b=-15 \end{gathered}

Therefore, you get that the equation of this line in Slope-Intercept Form is:


y=5x-15

Hence, the answer is: Last option.

User Vitalii Korsakov
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2.3k points