Question

How to find an equation for a line through two given points?​

Answer 1

The equation of the line is:
`y = 0.6x + 0.6`

Explanation:

Equation of a line:

The equation of a line has the following format:

`y = mx + b`

In which m is the slope and b is the y-intercept.

Two points:

We have these following two points in this exercise:

x = -6, y = -3, so (-6,-3)

x = 4, y = 3, so (4,3)

Finding the slope:

Given two points, the slope is given by the change in y divided by the change in x.

Change in y: 3 - (-3) = 3 + 3 = 6

Change in x: 4 - (-6) = 4 + 6 = 10

So

`m = (6)/(10) = 0.6`

Then

`y = 0.6x + b`

Finding b:

We replace one of the points in the equation to find b. I will use (4,3).

`y = 0.6x + b`

`3 = 0.6*4 + b`

`2.4 + b = 3`

`b = 0.6`

The equation of the line is:
`y = 0.6x + 0.6`