Question

there are 4 quarters for every one dollar and 10 dimes for every dollar. Without graphing, would the ratio of quarters to dollars appear to have a steeper line? Wxplain your reosoning

Answer 1

Answer:

no

Step-by-step explanation:

remember lines and line equations.

y = ax + b

a line has a slope indicating its angle relative to the basic coordinate axis and grid of x and y.

the slope is "a" in the generic equation, always the factor of x.

and it stands for the ratio y/x. it means how many units is y changing (and in what direction via its sign), when x changes a certain amount of units.

e.g. 3/4 means, when x changes 4 units to the positive (right) side, then y changes 3 units to the positive (up) side.

and also, when x changes 4 units to the negative (left) side, then y changes 3 units to the negative (down) side, as -/- is again +.

or -3/4 means, when x changes 4 units to the positive (right) side, then y changes 3 units to the negative (down) side, as -/+ is -.

and also, when x changes 4 units to the negative (left) side, then y changes 3 units to the positive (up) side, as +/- is again -.

so, we have here 2 ratios : 4/1 (quarters to dollars) and 10/1 (dimes to dollars).

remember what that means : y/x.

when x changes 1 unit to the right (x increases by 1), y changes 4 units up (y increases by 4).

and when x increases by 1 unit, y increases by 10 units.

what do you think is the steeper line ?

both are steep, as y increases much faster than x. but in the 10/1 ratio y increases much faster than in the 4/1 ratio. so, 10/1 is steeper than 4/1.

therefore, the answer is no. the ratio quarters to dollars does not represent a steeper line.

by the way, ratios like 4/1 or 10/1 are simply written 4 or 10.

so, when you see a line equation like y = 3x + 2,

you know the slope is 3 or actually 3/1.