How many solutions can be found for the linear equation? 10(x + 6) 2 - 9 = (15x + 1) 3 - 8
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Answer:
Linear Function
Step-by-step explanation:
If a function is linear then its slope is the same throughout the entire function
Slope of a linear function y = mx + c where m is the slope
The slope between any two points (x1, y1) and (x2, y2) is given by the ratio of the difference in y values to the difference in x values. This is referred to as rise/run
So slope = (y2-y1)/(x2-x1) for these two points
For the given table, we will let age correspond to the x values and height to the y values
Let's find the slope between all pairs of values
We can see that the difference in height between ages 3 and 5 is 6 (18-120 so the slope between these two points is (18-12)/(5-3) = 6/2 = 3
In a similar manner we can compute the slope between any two consecutive points
Between age = 5 and age = 6, height difference = 22-18=4 and slope is 4/1 = 4
Between age = 6 and age = 8, height difference = 30-22 = 8 and slope is 8/2 = 4
Between age = 8 and age = 11, height difference = 44-30 = 14 and slope is 14/3 = 4.6
While not exactly the same, the slope is almost the same for consecutive points
Therefore linear function (approximately)
The attached graph shows that the function plotted as a result of the table values shows an approximately linear relationship between age and height of tree
Note that I am only considering the values in the table for this and approximating. In reality there are many factors that affect the height of a tree
