A principal measures the weight of different numbers of textbooks that he finds in a storage room. The scatter plot below shows
the relationship between the weight, in pounds, and the number of textbooks. A line of best fit is drawn on the scatter plot.
Enter the slope of the line of best fit as a decimal to the nearest tenth.
Enter the slope of the line of best fit as a decimal to the nearest tenth.
1 answer:
The slope of the line of best fit is 2.4
Explanation:
To determine the slope of the equation, let us plot the coordinates in the slope form.
Analyzing the graph,some of the points that are on the straight line is (5,12) and (10,24)
Let us use the points (5,12) and (10,24) to find the slope of the line of best fit.
The formula for slope is
Substituting the coordinates (5,12) and (10,24), we have,
Subtracting, we get,
Dividing, we have,
Hence, The slope of the line of best fit is 2.4
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Answer:
the comparison must be reversed when multiplying by a negative
Step-by-step explanation:
The rules of equality apply to solving inequalities, with the exception that multiplication or division by a negative number reverses the sense of the comparison:
-x > 1
x < -1 . . . . . multiply both sides by -1
____
Effectively, multiplication (or division) by a negative number is equivalent to reflection across the origin. Things that were ordered left/right (on the number line) are ordered right/left after such a reflection:
-2 < -1
1 < 2
_____
<em>Additional comment</em>
Application of any function requires that you pay attention to ordering. Some functions naturally reverse the order; others do so only on specific domains.
Consider f(x) = 1/x.
1 < 2
f(1) > f(2) . . . . because the slope of the f(x) function is negative everywhere.
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<em>In the first and second quadrants</em>, the cosine function also reverses order.
20° > 10°
cos(20°) < cos(10°)
__
Probably the most commonly encountered function used with inequalities is the absolute value function.
|x-3| > 2
This function has one domain where the slope is negative, and another domain where the slope is positive.
For x < 3, the function negates its argument, so we have ...
-(x -3) > 2
-x +3 > 2
-x > -1
x < 1 . . . . . everywhere consistent with x < 3
For x ≥ 3, the function does nothing, so we have ...
x -3 > 2
x > 5
The solution to this absolute value inequality is (x < 1) ∪ (x > 5).
__
You can also resolve negative coefficients by adding the opposite. Addition and subtraction never require any change to the comparison operator.
-x > 1
0 > x +1 . . . . x is added
-1 > x . . . . . . -1 is added
