Question

What is the equation of the line with m = 6 that goes through the point (1, 4)?

Answer 1

Answer: B) y-4=6(x-1)

Substitute the point into each equation

A: y-4=6(x+1)

4-4=6(1+1)

4-4=6+6

0=12

This is false so it is not the answer

B: y-4=6(x-1)

4-4=6(1-1)

4-4=6-6

0=0

This is true so this is the answer, but I will continue solving just to check

C: y+4=6(x-1)

4+4=6(1-1)

4+4=6-6

8=0

This is false so it is not the answer

D: y+4=6(x+1)

4+4=6(1+1)

4+4=6+6

8=12
This is not true so it is not the answer

Your answer becomes b, the only true equation! Hope this helps comment below for more questions :)

Answer 2

Since it's a line we are talking about linear equation of a form

$f(x)=mx+n$

where $m$ is slope and $n$ is y-intercept.

Our particular line has a form of

$f(x)=6x+n$

So we are missing the y-intercept.

To find y-intercept $n$ we insert the coordinates of point $P(x,f(x))\to P(1,4)$ and solve for $n$

$4=6\cdot1+n \\n=-2$

So the final form of the line is

$y=6x-2$

Or as offered in the answers

$y-4=6(x-1)$

The answer is B.

Hope this helps.