Question

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

Answer 1

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.