Question

# Find the equation of a line that passes through and

Hint:

### We are given two points and we need to find the equation of the line passing through them. The equation of a line passing through two points (a, b) and (c, d) is

## 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.

Step by step solution:

Let the given points be denoted by

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

Expanding the factors, we have

Taking all the terms in the left hand side, we have

Finally, the equation of the line is

Dividing the equation throughout by 5, we get

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.