Answer:
Step-by-step explanation:
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:
There are two ways to do this
Method 1:
Find (f-g)(x) first
(f-g)(x) = f(x) - g(x)
(f-g)(x) = (5x^2+3) - (-2x+4)
(f-g)(x) = 5x^2+3+2x-4
(f-g)(x) = 5x^2+2x-1
Then plug in x = -3
(f-g)(-3) = 5(-3)^2+2(-3)-1
(f-g)(-3) = 5(9)+2(-3)-1
(f-g)(-3) = 45-6-1
(f-g)(-3) = 39-1
(f-g)(-3) = 38
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Method 2:
Find f(-3)
f(x) = 5x^2+3
f(-3) = 5(-3)^2+3
f(-3) = 5(9)+3
f(-3) = 45+3
f(-3) = 48
Find g(-3)
g(x) = -2x+4
g(-3) = -2(-3)+4
g(-3) = 6+4
g(-3) = 10
Subtract the two results
(f-g)(-3) = f(-3) - g(-3)
(f-g)(-3) = 48 - 10
(f-g)(-3) = 38
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Whichever method you pick, the answer is: 38