Question

Write the equation of the line that passes through the points (3, 7) and (-1, 2)

Answer 1

`y = (5)/(4) x + 3 (1)/(4)`

Explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

Let's find the gradient of the line, m, first.

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

`m = (7 - 2)/(3 - ( - 1)) \\ m = (5)/(3 + 1) \\ m = (5)/(4)`

`y = (5)/(4) x + c`

To find the value of c, substitute a coordinate.

when x= -1, y= 2,

`2 = (5)/(4) ( - 1) + c \\ c = 2 + (5)/(4) \\ c = 3 (1)/(4)`

Thus, the equation of the line is

`y = (5)/(4) x + 3 (1)/(4)`