Find the equation of a line that passes through  and 

The correct answer is: 3x + y + 8 = 0

 
Step by step solution:
Let the given points be denoted by

(a, b) = (-3, 1)

(c, d) = (2, -14)
The equation of a line passing through two points (a, b) and (c, d) is

 
Using the above points, we have

 
Simplifying the above equation, we have

 

Cross multiplying, we get

5(y + 14) = -15(x - 2)
Expanding the factors, we have

5y + 70 = -15x + 30
Taking all the terms in the left hand side, we have

15x + 5y + 70 - 30 = 0
Finally, the equation of the line is

15x + 5y + 40 = 0
Dividing the equation throughout by 5, we get

3x + y + 8 = 0
This is the required equation.
 

We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by ax + by + c = 0,, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc.