Question

What is the equation of the line that passes through the point (4,1) and has a slope of 4?

Answer 1

Recall that the point-slope form of a line is of the form y=mx+b. We are told that the point (4,1) is on our line and that the slope is 4. This means that m=4. So far, we have the equation

$y=4x+b$

So it only suffices to find the value of b.

Since (4,1) is on this line, it should happen that if we replace x by 4, it must happen that y is 1.

Then, we have the following

$1=4\cdot4+b\text{ = 16+b}$

So, if we subtract 15 on both sides, we get

$b=1-16=-15$

Then the equation of the line is

$y=4\cdot x-15$