Question

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

Answer 1

Step-by-step 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

If you like to venture further, do check out my insta (learntionary) where I constantly post math tips! Thanks!

Answer 2

Answer:

$y-\frac{1}{3} =\frac{3}{4} (x-4)$

Step-by-step 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 $\frac{1}{3}$ and 4 respectively.

Now we can decide between 2 and 4 by plugging in the point $(4,\frac{1}{3})$ to see which works properly.

Simplify equation 2

$y-\frac{1}{3} =\frac{3}{4} (x-4)\\\\y-\frac{1}{3} =\frac{3}{4}x-3\\\\y=\frac{3}{4}x-\frac{8}{3}$

Plug in the point

$\frac{1}{3} =\frac{3}{4}(4)-\frac{8}{3} \\ \\\frac{1}{3} =3-\frac{8}{3} \\\\\frac{1}{3} =\frac{9}{3} -\frac{8}{3} \\\\\frac{1}{3} = \frac{1}{3}$

This checks out, so equation 2 is your answer.