Question

Write an equation in point slope form that is parallel to AB with endpoints A (2, -1) and B (4, 5) that goes through the point (1.5, 4)

Answer 1

`y = 3x - 0.5`

Explanation:

Given

Goes through

`C = (1.5,4)`

Parallel to AB

`A = (2,-1)`

`B = (4,5)`

Required

Determine the line equation

First, calculate the slope of AB

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (5--1)/(4-2)`

`m = (6)/(2)`

`m = 3`

The line is said to be parallel to AB. This implies that their slopes are equal.

The equation of the line is then calculated as:

`y = m(x - x_1) + y_2`

Where:

`(x_1,y_1) = (1.5,4)`

So:

`y = 3*(x - 1.5) + 4`

`y = 3x - 4.5 + 4`

`y = 3x - 0.5`