Respuesta :

lauren6751
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 :)
r3t40

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

[tex]f(x)=mx+n[/tex]

where [tex]m[/tex] is slope and [tex]n[/tex] is y-intercept.

Our particular line has a form of

[tex]f(x)=6x+n[/tex]

So we are missing the y-intercept.

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

[tex]

4=6\cdot1+n \\

n=-2

[/tex]

So the final form of the line is

[tex]y=6x-2[/tex]

Or as offered in the answers

[tex]y-4=6(x-1)[/tex]

The answer is B.

Hope this helps.

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