Hello. If I have the following table:
Time(x) 18 27 72 81
Distance (y) 8 12 32 36
How would I create an equation relating the variables in the table?
y=
Please help. I have never done this before?
check for a common ratio of changes. For example,
(12-8)/(27-18) = 4/11
(32-12)/(72-27) = 20/55 = 4/11
so, it appears that the line has a constant slope of 4/11
Now, using any of the given points, plug into the point-slope form of a line:
y-8 = 4/11 (x-18)
or
11y-88 = 4x-72
11y = 4x+16
y = (4x + 16)/11
etc.
To be thorough, though, you might want to check the other intervals. If the slope changes, then the equation will not be so simple.
d = r * t.
8 = r * 18, r = ?.
12 = r * 27, r = ?.
32 = r * 72, r = ?.
I made a typo.
Maybe Henry's solution will be better. Either approach will work if done carefully.
Steve's slope calculations should have resulted in 4/9
so continue with:
y-8 = (4/9)(x-18)
To create an equation relating the variables in the table, you need to analyze the relationship between the time (x) and the distance (y).
Let's observe the change in distance corresponding to the change in time:
From x = 18 to x = 27, the distance increases from y = 8 to y = 12.
From x = 72 to x = 81, the distance increases from y = 32 to y = 36.
Notice that the change in distance (y) is equal to 4 when the change in time (x) is 9. This indicates a constant rate of change in distance with respect to time.
To find the equation relating x and y, we can calculate the slope (m) using the formula:
m = (change in y) / (change in x)
m = (12 - 8) / (27 - 18)
= 4 / 9
Now we have the slope (m) of the equation.
To find the y-intercept (b), we can use the point (x, y) from the table. Let's use (18, 8).
Using the point-slope form of a linear equation (y = mx + b), we can substitute the values to find b:
8 = (4/9) * 18 + b
Now, let's solve the equation for b:
72/9 = 8/9 + b
64/9 = b
So, the equation relating x and y is:
y = (4/9)x + (64/9)
Therefore, the equation relating time (x) to distance (y) is:
y = (4/9)x + (64/9)