Question

AB contains points (2, 1) and (-1, -8). What is the equation of the line parallel to AB that contains point (0, 2)?

Answer 1

For this case we have that by definition, the equation of a line in 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

We have two points that belong to the AB line:

$(x_ {1}, y_ {1}) :( 2,1)\\(x_ {2}, y_ {2}): (- 1, -8)$

We can find the slope:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-8-1} {- 1-2} = \frac {-9} {- 3} = 3$

By definition, if two lines are parallel then their slopes are equal. Thus, a line parallel to AB will have slope $m = 3$, then the equation will be of the form:

$y = 3x + b$

We substitute the given point and find b:

$(x, y) :( 0,2)\\2 = 3 (0) + b\\2 = b$

Finally, the equation is:

$y = 3x + 2$

Answer:

$y = 3x + 2$