Maths-
General
Easy

Question

# Find the equation of a line that passes through  and

Hint:

## 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 get5(y + 14) = -15(x - 2)Expanding the factors, we have5y + 70 = -15x + 30Taking all the terms in the left hand side, we have15x + 5y + 70 - 30 = 0Finally, the equation of the line is15x + 5y + 40 = 0Dividing the equation throughout by 5, we get3x + y + 8 = 0This 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.