Question

find the equation of a straight line passing through the point (1,2) and making an intercept of 3 on the positive y-axis.​

Answer 1

Given: the points (1|2) and (0|3) lie on the line.

Question: equation of the line.

Solution:

General equation of a line: y = kx+d,

whereby:

the point (y|x) lies on the line
When x = 0, y = d
The point (0|3) says that d = 3.

So far, the equation is y = kx +3 ……… (1)

Inserting the point (1|2) into (1):

2 = k(1) + 3 => 2–3=k => -1 = k

Putting k into (1):

y = -1x + 3 => y = -x + 3 => y = 3 - x

Answer:

y = 3 - x