If y varies directly with x and y=8 when x=3, what is the value of y when x is 9 ?

Question

its an algebra 9th grade problem

Answer 1

For direct proportionality, the basic equation is y = kx, where k is a proportionality constant. If you plug in the given point (3,8), you will find: 8 = k(3), so k = 8/3 Now use the value of k to solve for the unknown y value if x = 9. y = (8/3)*9 = 24 It's the same answer Mark got using a proportion, just a different way to look at the problem. As a side note, technically, this problem requires you to make the assumption that the proportionality has the form of y = kx rather than y = mx + b which is the true formula for a direct proportion. You can't solve for b without knowing two points on the line, so this problem is slightly flawed from that perspective and really could have multiple answers since there are an infinite number of lines (meaning a proportional relationship) that could have a slope of 8/3.

Answer 2

Using a proportion:

8 / 3 = y / 9           multiply both sides by 9

72 / 3 = y              simplify

24 = y

 

Without algebra:

 

Since 9 is three times 3, y would be three times 8, or 24.