Question

What is the equation of the line passing through `(13,3)` and `(0,-2)`?

Answer 1

`y = 5/13x -2`

Explanation:

There are several methods of finding the equation of a line though two given points:

Method 1. Find the slope, then use one point and the slope to find c.

Method 2. Find the slope and use one point to find the equation using the formula: `y-y_1 = m(x-x_1)`

Method 3. Make simultaneous equations using the two points and solve them to find the values of m and c

Method 4. Use the formula which uses two given points.

Let's use method 4 with given points: `(13,3)` and `(0,-2)`

`(y-y_1)/(x-x_1) = (y_2 -y_1)/(x_2-x_1)`

`(y-(-2))/(x-0) = (3-(-2))/(13-0) = 5/13`

`(y+2)/x = 5/13" cross multiply"`

`13y + 26 = 5x`

`13y = 5x-26`

`y = 5/13x -2" is the required equation"`