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).
y = 5x − 15
y = 5x + 15
y = 1 over 5x + 21 over 5
y = 1 over 5x − 29 over 5

Answer 1

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

On the other hand, we have that if two lines are parallel then their slopes are equal.

Given the line AB: $y = 5x + 1,$ the slope is $m_ {1} = 5$

Therefore, a parallel line will have slope $m_ {2} = 5.$

Thus, the equation is of the form is: $y = 5x + b$

We substitute point$(4,5)$and find "b":

$5 = 5 (4) + b\\5 = 20 + b\\5-20 = b\\b = -15$

Finally, a line parallel to line AB is: $y = 5x-15$

Answer:

$y = 5x-15$