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How would you write a linear equation in slope-intercept form to model a tree 4 feet tall that grows 3 inches per year?
Wiki User
∙ 13y ago
Slope intercept form is y=mx+b, with m indicating slope (also known as rate of change) and b indicating the y-intercept. In this case, the y would indicate the height of the tree.
Since the tree grows at 3 inches per year, we could label the y-axis in inches (most likely using multiples of 12). However, since 3 inches can easily be thought of as 1/4 foot, let's label the y-axis in feet. Now we have x = years and y = height in feet (both labeled 1, 2, 3, etc.) , and we know our rate of change is 1/4 foot per year (or 1/4x). We know the tree starts out at 4 feet, so that point on our graph is (0,4) which is the y-intercept (the place where our line crosses the y-axis).
Thus, the y-intercept equation is y = 1/4x + 4 .
Since we know one point and the slope, another way would be to use the point slope method:
y-y1=m(x-x1)
y-4=1/4(x-0)
y-4=1/4x
y=1/4x+4
Not really worthwhile when the problem itself gives us all we need.
Of course, if we used inches for our y-axis, our point would have been (0,48) and the slope would have been 3, so our formula would have been y=3x+48 .
Wiki User
∙ 13y ago
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