Answer:
[tex]y = 3x - 0.5[/tex]
Step-by-step explanation:
Given
Goes through
[tex]C = (1.5,4)[/tex]
Parallel to AB
[tex]A = (2,-1)[/tex]
[tex]B = (4,5)[/tex]
Required
Determine the line equation
First, calculate the slope of AB
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{5--1}{4-2}[/tex]
[tex]m = \frac{6}{2}[/tex]
[tex]m = 3[/tex]
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:
[tex]y = m(x - x_1) + y_2[/tex]
Where:
[tex](x_1,y_1) = (1.5,4)[/tex]
So:
[tex]y = 3*(x - 1.5) + 4[/tex]
[tex]y = 3x - 4.5 + 4[/tex]
[tex]y = 3x - 0.5[/tex]
