Question

How do you write the standard form of a line given (2.3) and (4,5)?

Answer 1

The standard form of a straight line is `y=ax+b`, if the line is not horizontal or vertical.

Explanation:

To determine the standard form of the line we need to find the value of the parameters `a` and `b`. We know that the line passes through the points `(2,3)` and `(4,5)`, so both points satisfy the line equation. That is:

`3=a2+b`, because of the first point, and
`5=a4+b`, because of the second point. Then, subtracting the second minus the first, we get:
`2=2a`, and so `a=1`. Substituting in either equation (say the first one), we get:

`3= 2*1+b` and so `b=1`. The standard form of the straight line is:

`y=1x+1=x+1`