Question

Which of the following line passes through point (-4,5) and is parallel to the line segment whose endpoints are at (-2,-3) and (2,5)?

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

By definition, if two lines are parallel then their slopes are equal.

Then, the requested line will have a slope equal to:

`m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {5 - (- 3)} {2 - (- 2)} = \frac {5 +3} {2 + 2} = \frac {8} {4} = 2`

Thus, the line is of the form:

`y = 2x + b`

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

`5 = 2 (-4) + b\\5 = -8 + b\\5 + 8 = b\\b = 13`

Finally, the equation is:
`y = 2x + 13`

Answer:

`y = 2x + 13`