Answer:
hope this helps!! :)
Explanation:
Proportional relationships are essentially two things that change at the same time, and in direct relationship with each other.
For this graph, as we increase t by 3, we increase d by 8.
We can start off by plotting some logical points.
(d and t are usually used to mean distance and time in science, and I will use this example because it is intuitive)
If I haven't increased the t at all (if no time has passed), the d also couldn't increase (if I haven't had any time to travel, then I couldn't have traveled any distance either)
So, we know that if t = 0, d also must = 0. This can be our first point
(t is along the x-axis, and d is along the y-axis. points are written as (x value, y value). So, these points are written in (t value, d value) because that is the cause and effect relationship)
So, we have a point at (0, 0).
Now, if we increase the t by 3, we increase the d by 8. So, if we add
+ 3 to t, we need to add +8 to d.
( 0 , 0 )
+ 3 = + 8
( 3 , 8 )
So, we have a point at (3, 8)
Following this same logic (we increase t by 3 and d by 8), we have another point at (6, 16).
This is harder to think of intuitively, but what if we were to subtract 3 t? If, from 0, 0, we decreased t by 3, we should also decrease d by 8
giving us another point as (-3, -8).
We have enough points to easily graph this graph (we know it will look like a line because they both increase/decrease at the same time).
{there are arrows on the end because we could theoretically keep adding +3 and +8 or -3 and -8 forever}.
To find the unit rate of change, we have 2 methods. The first, which is less precise, is that we can look at where the d-value is at our t-value.
(look at 1 and see how high the line is)
The more precise way to calculate it is to find the relationship between an increase of 3 and an increase of 1. We know that 1 is one-third of 3
(3 / 1 = 3). So, we must find what one-third of 8 would.
3 ÷ 3 = 1
8 ÷ 3 = 2.667 {technically, this decimal goes on forever, but we round it}
(or, it would be more precise to write your answer as 8 / 3
