Up and Running Auto Shop keeps track of their regular customers' data to see if there is a relationship between the life of a ca
r's engine (y) and the number of times the oil is changed (x). When the data is shown on a scatter plot, the equation for the line of best fit is y = 0.4125x + 0.1576. What is the relationship between 0.4125 and the life of the car's engine?
2 answers:
Answer:
Strong and Positive Relation
Step-by-step explanation:
Here, when we plot the graph of y = 0.4125x + 0.1576
Then we see that the graph has a positive correlation as we increase the value of x, the value of y is also increasing. So, Life of Car's Engine and Number of Times the Oil is Changed has a Positive relation.
And if our scatter plot is horizontal, vertical or we unable to draw the line of best fit then it has no or little correlation but here we see that line is not lie in either case. So, the relationship is strong but not very strong.
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General Idea:
When a point or figure on a coordinate plane is moved by sliding it to the right or left or up or down, the movement is called a translation.
Say a point P(x, y) moves up or down ' k ' units, then we can represent that transformation by adding or subtracting respectively 'k' unit to the y-coordinate of the point P.
In the same way if P(x, y) moves right or left ' h ' units, then we can represent that transformation by adding or subtracting respectively 'h' units to the x-coordinate.
P(x, y) becomes . We need to use ' + ' sign for 'up' or 'right' translation and use ' - ' sign for ' down' or 'left' translation.
Applying the concept:
The point A of Pre-image is (0, 0). And the point A' of image after translation is (5, 2). We can notice that all the points from the pre-image moves 'UP' 2 units and 'RIGHT' 5 units.
Conclusion:
The transformation that maps ABCD onto its image is translation given by (x + 5, y + 2),
In other words, we can say ABCD is translated 5 units RIGHT and 2 units UP to get to A'B'C'D'.