Part A)
Given
Using the point-slope form of the line equation
where
m is the slope of the line
(x₁, y₁) is the point
In our case:
substituting the values m = 6 and the point (x₁, y₁) = (7, 2) in the point-slope form of the line equation
Therefore, the equation in point-slope form for the line having the slope m = 6 and containing the points (7,2) will be:
Part B)
Given
Using the point-slope form of the line equation
where
m is the slope of the line
(x₁, y₁) is the point
In our case:
substituting the values m = -3 and the point (x₁, y₁) = (3, 8) in the point-slope form of the line equation
Therefore, the equation in point-slope form for the line having the slope m = -3 and containing the points (3, 8) will be:
The option (C) Mus. Apt. = -22.26 + 0.4925(IQ score) is correct because the value of slope is 0.4925 and y-intercept is -22.26.
<h3>What is the line of best fit?</h3>
A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have data shown in the picture.
Let's suppose the regression line is:
y = mx + c
Where m is the slope of the regression line and c is the y-intercept of the line.
We can calculate the value of m and c by using the formula.
After calculating, we get:
m = 0.4925
c = -22.26
Mus. Apt. = 0.49253(IQ score) - 22.26
or
Mus. Apt. = -22.26 + 0.4925(IQ score)
Thus, the option (C) Mus. Apt. = -22.26 + 0.4925(IQ score) is correct because the value of slope is 0.4925 and y-intercept is -22.26.
Learn more about the line of best fit here:
brainly.com/question/14279419
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Q = -60 and P ≠ 32 will result in an equation with no solutions. (Both conditions must be met.)
_____
For Q = -60 and P = 32, there will be an infinite number of solutions. For any other values of Q and P, the solution is
.. x = (32 -P)/(Q +60)
(f-g)(x) = f(x) - g(x)
= (x^3 -2x+6) - (2x^3+3x^2-4x+2)
= x^3 -2x +6 -2x^3 -3x^2 +4x -2 . . . . distribute the negative sign
= (1-2)x^3 -3x^2 +(-2+4)x +(6-2) . . . . . combine like terms
(f-g)(x) = -x^3 -3x^2 +2x +4
