Point slope question?

Question

I have problems with this type of problem...so please explain step by step how you derive the answer...

Find an equation of a line that passes through the point and has the indicated slope:
(4, 5/2) m=4/3

the given answer is:
8x-6y-17=0

Answer 1

Use the point-slope form: (y -y1) = m(x - x1)

where m is the slope, anx (x1, y1) is the point. x and y are the variables. So just plug in your data:

If (x1, y1) = (4, 5/2) and m = 4/3, then

(y - 5/2) = 4/3(x - 4)
y - 5/2 = 4x/3 -16/3
6y - 15 = 8x = 32 (multiplying by 6 to clear fractions)
8x - 6y = -15 + 32
8x -6y - 17 = 0

Answer 2

Start with the point-slope formula of a line: y=mx+b
then substitute m = 4/3 in and also use your point (4, 5/2) for the x-value and the y value.
That gives you 5/2=(4/3)(4) + b and it allows you to figure out the y intercept (b)!
Mulitply both sides by 6 and you get b=-17/6
Then to put it in standard form, you just take b and m and put them back into a new point-slope formula y=4/3x -17/6.

Again multiply both sides of your equation by 6 and you get 6y = 8x - 17 which you can easily rearrange to get your anwer.

Answer 3

Point slope form is (y-y1)=m(x-x1). So then you replace the slope (m) for m. so now you have (y-y1)=4\3(x-x1). Then you replace x1 and y1 with 4 and 5\2(or 2.5). (y-5\2)=4\3(x-4).... (y-5\2=4\3x-16\3.... y+17\6=4\3x, then you multipy the whole equation by -6. -6(y+17\6=4\3x).... -6y-17=-8x.. make the equation equal to zero and your answer is..... 8x-6y-17=0

Answer 4

(y-5/2) / (x-4) = (4) / (3)
cross multiply

3(y-5/2) = 4(x-4)
3y-15/2 = 4x=16

multiply by two to eliminate fractions
6y-15= 8x-32

add 15 to both sides
6y = 8x-17
-8x + 6y = -17
factor a neg one out of it all, then subtract 17 from both sides

8x-6y-17=0