Question

Which equation represents a line that passes through (4, 1/3) and has a slope of 3/4?

Answer 1

Explanation:

let the equation be y - y1 = 3/4(x - x1)

sub (4, 1/3):

y - 1/3 = 3/4(x - 4)

therefore answer is option 2.

Topic: coordinate geometry

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Answer 2

`y-(1)/(3) =(3)/(4) (x-4)`

Explanation:

To see which equations have the slope of 3/4, we just need to focus on the right half of the equations to see what the multiplier of x is.

Equations 1 and 3 can be eliminated because they have a slope of
`(1)/(3)` and 4 respectively.

Now we can decide between 2 and 4 by plugging in the point
`(4,(1)/(3))` to see which works properly.

Simplify equation 2

`y-(1)/(3) =(3)/(4) (x-4)\\\\y-(1)/(3) =(3)/(4)x-3\\\\y=(3)/(4)x-(8)/(3)`

Plug in the point

`(1)/(3) =(3)/(4)(4)-(8)/(3) \\ \\(1)/(3) =3-(8)/(3) \\\\(1)/(3) =(9)/(3) -(8)/(3) \\\\(1)/(3) = (1)/(3)`

This checks out, so equation 2 is your answer.