What is the linear equation for the following table?
x h(x)
20 20
40 -100
60 -220
80 -340
100 -460
(-100-20)/(40-20) = -6
so, the slope is -6, and we start with
h = -6x
But -6(20) = -120, and h(20) = 20. So
h(x) = -6x + 140
You can check to make sure this fits the other points as well.
Thank you so much @steve
To find the linear equation for the given table, we need to determine the relationship between x and h(x), where x is the independent variable and h(x) is the dependent variable.
From the table, we observe that as x increases by 20, h(x) decreases by 120. This suggests that there is a constant rate of change between x and h(x).
To find the constant rate of change, we can select any two points from the table and use them to calculate the slope. Let's choose the first and last points (20, 20) and (100, -460).
The slope (m) can be calculated using the formula:
m = (change in h(x)) / (change in x)
In this case, the change in x is 100 - 20 = 80, and the change in h(x) is -460 - 20 = -480. Thus, the slope is:
m = (-480) / (80) = -6
Now that we have the slope, we can find the y-intercept (b) by substituting the coordinates of one of the points (20, 20) into the slope-intercept form of a linear equation:
y = mx + b
Using the point (20, 20), we have:
20 = (-6)(20) + b
20 = -120 + b
b = 140
Therefore, the linear equation for the given table is:
h(x) = -6x + 140