Question

What is an equation of the line that passes through the points (2, -7) and (8, -4)?

Answer 1

The answer is

`y = (1)/(2) x - 8`

Explanation:

To find the equation of the line that passes through two points , first find the slope and then use the formula

y - y1 = m(x - x1)

where m is the slope

(x1 , y1) are any of the points

To find the slope of the line using two points we use the formula

`m = (y2 - y1)/(x2 - x1)`

Slope of the line using points

(2, -7) and (8, -4) is

`( - 4 + 7)/(8 - 2) = (3)/(6) = (1)/(2)`

Now the equation of the line using point (2 , - 7) and slope 1/2 is

`y + 7 = (1)/(2) (x - 2)`

`y + 7 = (1)/(2) x - 1`

`y = (1)/(2) x - 1 - 7`

We have the final answer as

`y = (1)/(2) x - 8`

Hope this helps you