Which statement is always true?
a. a linear relationship is proportional.
b. a linear relationship is non-proportional.
c. a proportional relationship contains the point ( 0 , 0 ) .
d. a non-proportional relationship has a constant rate of change.

A

Step-by-step explanation:

When we say proportional, we basically mean two quantities are based on a multiplicative constant. For example:

1:2 is proportional to 5:10, because if we reduce 5:10, we get 1:2.

Also, in terms of coordinate geometry, we can say line

y = ax

and

y = bx

are proportional if a:b = constant always.

We say that is a linear line. Linear relationship.

Now, looking at the answer choices, we can eliminate B and C [Choice C is easily eliminated because point (x,y) doesn't matter]. Also, we ccan eliminate D because this is just the opposite.

So answer choice A holds true.

A is right.

it's

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.