Question

Which equation represents a line that has a slope of 3/4 and passes through the point (2,1)?
1.) 3y=4x-5 3.) 4y=3x-2
2.) 3y=4x+2 4.) 4y=3x+5

Answer 1

(x,y) = (2,1) just plug in x and y and see which is true

Answer 2

You can eliminate a number of choices by plugging in (2,1) and seeing if you end up with a true statement. For the rest, rearrange the formula into slope intercept form \(y=mx+b\) and look for the one with a slope of \(\frac{3}{4}\).

Answer 3

@zpupster there are multiple equations which pass through (2,1) here :-)

Answer 4

Alternatively, you could rearrange the equation first, then check the remaining candidates to see if they go through (2,1). Which to do depends on whether you are better at doing algebra or arithmetic quickly.

Answer 5

Or, if you are a pattern matching fiend, you could observe that doing the first and second things together gives you two overlapping sets, with the intersection being the correct answer :-)

Answer 6

could you explain that to me sorry.

Answer 7

Okay. We can see that half of the answer choices fail the test of passing through (2,1) because when you plug in (2,1) as (x,y) you get something like 3 = 10.

A little thought will tell you that half of the answer choices aren't going to have a slope of 3/4 because the ratio of the x coefficient to the y coefficient isn't 3:4.

If you look at the intersection of those two sets, you'll find the one choice which both has a slope of 3/4 and which passes through (2,1).