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Answer:
1)
2)
3)
Step-by-step explanation:
We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.
1)
First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:
Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:
Subtract. So, our slope is:
2)
Now, let's use the point-slope form:
We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:
Simplify. So, our point-slope equation is:
3)
Finally, we want to convert this into slope-intercept form. So, let's solve for our y.
On the right, distribute:
Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:
Subtract. So, our slope-intercept equation is:
And we're done!
We can plot this data on MS Excel and determine the distribution of these data reflected on the graph. Among these numbers, 50 is the outlier since it is very far from the other numbers ranging from 76 to 83. We can perform interquartile range to determine or verify the outliers in the data set. In this respect, we can see that there is not much distribution seen. The average of all data sets is equal to 96.25. When the outlier (50) is removed, we expect the mean to become higher since a low number was ommitted including high numbers only. Outliers are obtained from special causations such as human errors.
