Question

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

Answer 1

Explanation:

B

Answer 2

We can use the point-slope equation:

`y = mx + b`
m, the slope, is 3/4:

`y = (3)/(4) x + b`
To find b, we plug in the point (4,1/3):

`( (1)/(3) ) = (3)/(4) (4) + b \\ (1)/(3) = 3 + b \\ (1)/(3) = (9)/(3) + b`

`- (8)/(3) = b`

Therefore, the point-slope equation is

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

Now we have to see which answer matches.



`y - (3)/(4) = (1)/(3) (x - 4) \\ y - (3)/(4) = (1)/(3) x - (4)/(3) \\ y - (9)/(12) = (1)/(3) x - (16)/(12)`

`y = (1)/(3) x - (7)/(12)`
Since this is not the same, we try the next one.



`y - (1)/(3) = (3)/(4) (x - 4) \\ y - (1)/(3) = (3)/(4) x - 3 \\ y - (1)/(3) = (3)/(4) x - (9)/(3)`

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

This is the same, so this is the answer. We should still double-check the other answers.


`y - (1)/(3) = 4(x - (3)/(4) ) \\ y - (1)/(3) = 4x - 3 \\ y - (1)/(3) = 4x - (9)/(3)`

`y = 4x - (8)/(3)`
This one is not equivalent.


`y - 4 = (3)/(4) (x - (1)/(3) ) \\ y - 4 = (3)/(4) x - (1)/(4) \\ y - (16)/(4) = (3)/(4) x - (1)/(4)`

`y = (3)/(4) x + (15)/(4)`
This one also does not work.


The answer is the second one:

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