Question

Suppose y varies at a constant rate of change of 0.5 with respect to x (so that Δ y = 0.5 ⋅ Δ x ), and y = 1.5 when x = 3 .

Answer 1

The rate of change of y with respect to x is 0.5, and it can be used to calculate the change in y for a given change in x.

Step-by-step explanation:

The question is asking about the rate of change of y with respect to x when the rate is constant at 0.5. In this case, the change in y (Δy) is equal to 0.5 times the change in x (Δx).

Given that y = 1.5 when x = 3, we can use the rate of change equation to find the change in y when the change in x is known. For example, if Δx is 2, then Δy would be 0.5 times 2, which is 1. So, when x increases from 3 to 5, y would increase from 1.5 to 2.5.

Answer 2

Answer and explanation:

Given the above, we find y in terms x

change in y change in x = 0.5

The formula for a straight line is y= mx+b where m is slope of the line and b is the y intercept

We substitute given values above in the straight line equation:

y=mx+b

1.5= 0.5×3+b

1.5=1.5+b

b= 0

y in terms of x for the line is therefore given by the formula :

y=0.5x+0