Answer:
The line equation that passes through the given points is 5x – 2y + 16 = 0
Explanation:
Given:
Two points are A(-2, 3) and B(0, 8).
To find:
The line equation that passes through the given two points.
Solution:
We know that, general equation of a line passing through two points (x1, y1), (x2, y2) is given by
[tex]\frac{(y- y1)}{(x-x_1)}= \frac{((y_2- y_1)}{(x_2- x_1 )}[/tex]
[tex]{(y- y1)= \frac{((y_2- y_1)}{(x_2- x_1 )}\times(x-x_1)[/tex].............(1)
here, in our problem x1 = 0, y1 = 8, x2 = -2 and y2 = 3.
Now substitute the values in (1)
[tex]y-8 = \frac{(3-8)}{(- 2 - 0)}\times(x- 0)[/tex]
[tex]y-8 = \frac{(- 5)}{(-2)}\times(x)[/tex]
[tex]y-8 =\frac{5}{2}x[/tex]
2y – 16 = 5x
5x – 2y + 16 = 0
Hence, the line equation that passes through the given points is 5x – 2y + 16 = 0.
