Question

how to find the equation of the tangent line if you already have the slope?

Answer 1

plug your slope for the point youre triyng to find in point-slope formula:
y-y1=m(x-x1) where m is the slope and (x1,y1) is a point

Answer 2

ok im not sure to understand

Answer 3

i got the slope 6x and the point that u want to verify is (1,3)

Answer 4

so i plug 1 into 6x , which equals 6 and than?

Answer 5

help with this one?

Answer 6

yes please!

Answer 7

okay so you take the point slope formula which is f(x)-y1=m(x-x1) and your point is (1,3) so x1=1 and y1=3. Plug those in and what do you get?

Answer 8

Ok well youre slope is 6 and the point is at (1,3).. so plug this into y-y1=m(x-x1) m is the slope and x1,y1 is the point.. So here....
y-3=6(x-1) is youre answer. Does that make sense? you just basically use this formula

Answer 9

uhmm ok so 6x+3?

Answer 10

but im not sure to understand to formula

Answer 11

well its y=6x-3 because
distribute the 6
y-3=6x-6
add three to both sides
y=6x-3

Answer 12

i dont understand

Answer 13

The formula:\[y-y _{1}=m(x-x _{1})\]
where \[(x _{1},y _{1})\] is the point you know and \[m\] is the slope of the tangent line

Answer 14

ok

Answer 15

You know the slope which is 6 so m=6 and the point is (1,3) so x1=1 and y1=3. got it so far?

Answer 16

yeah

Answer 17

Now take the m the x1 and the y1 and put them in the equation \[y-y _{1}=m(x-x _{1})\]
becomes
\[y-3=6(x-1)\]

Answer 18

ok yeah

Answer 19

then y-3=6x-6 by distribution, add 3 to both sides and you have y=6x-3

Answer 20

oh ok that<s quite simple

Answer 21

thank u!

Answer 22

No problem. If you have any more questions let me know

Answer 23

ok yeah thank u :)