Question

Find the equation of the straight line through (3,4) and (5,6).

Answer 1

y= x+1

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.

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

Using the above formula,

Gradient

`= (6 - 4)/(5 - 3) \\ = (2)/(2) \\ = 1`

Thus m=1. Substitute m=1 into the equation:

y= 1x +c

y= x +c

Susbt. a coordinate.

When x=3, y=4,

4= 3 +c

c= 4-3

c=1

Thus, the equation of the line is y= x+1.