Write equation of the line containing (-3, 4) and (-1, -2)

The correct answer is: 3x + y + 5=0

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

(a, b) = (-3, 4)

(c, d) = (-1, -2)
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

2(y + 2) = -6(x + 1)
Expanding the factors, we have

2y + 4 = -6x - 6
Taking all the terms in the left hand side, we have

6x + 2y + 4 + 6 = 0
Finally, the equation of the line is

6x + 2y + 10 = 0
Dividing the equation throughout by2, we get

3x + y + 5 = 0
This is the general form of the equation.
This is also 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.