Describe how to determine the average rate of change between x = 3 and x = 5 for the function f(x) = 3x3 + 2. Include the averag
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A. The equation of the line is y = -0.2 x + 1.9
B. The equation of the line is y = 4 x + 3
C. The equation of the line is y = -8
D. The equation of the line is y = 2 x + 4
Step-by-step explanation:
The slope-intercept form of the equation of a line is y = m x + b, where
m is the slope of the line and b is the y-intercept
- The formula of the slope of a line which passes through points
and
is
- The slope of a horizontal line whose equation y = b is zero
- The y-intercept means the line intersect the y-axis at point (0 , b)
A.
∵ The line passes through points (2 , 1.5) and (-5 , 36.5)
∴ = 2 and
= -5
∴ = 1.5 and
= 36.5
∵
∴
∴ m = -0.2
∵ y = m x + b
∵ m = -0.2
∴ y = -0.2 x + b
- To find b substitute x and y in the equation by the coordinates of
one of the two given points
∵ x = 2 and y = 1.5
∴ 1.5 = -0.2(2) + b
∴ 1.5 = - 0.4 + b
- Add 0.4 to both sides
∴ 1.9 = b
∴ y = -0.2 x + 1.9
The equation of the line is y = -0.2 x + 1.9
B.
∵ m = 4
∵ y = m x + b
∴ y = 4 x + b
∵ Point (3 , 15) lies on the line
- To find b substitute x and y in the equation by the coordinates
of the given point
∵ x = 3 and y = 15
∴ 15 = 4(3) + b
∴ 15 = 12 + b
- Subtract 12 from both sides
∴ 3 = b
∴ y = 4 x + 3
The equation of the line is y = 4 x + 3
C.
∵ The line has the same slope of line y = 1
- The line whose equation y = 1 is a horizontal line
∵ The slope of the line y = 1 is zero because it is a horizontal line
∴ m = zero
∵ y = m x + b
∴ The equation of the line is y = (0)x + b
∴ y = b
∵ The line passes through point (3 , -8)
- In the horizontal line the y-coordinates of all point lie on the line
are equal
∴ The line intersect the y-axis at point (0 , -8)
∴ b = -8
∴ y = -8
The equation of the line is y = -8
D.
∵ m = 2
∵ y-intercept is at point (0 , 4)
∴ b = 4
∵ y = m x + b
∴ y = 2 x + 4
The equation of the line is y = 2 x + 4
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You can learn more about the linear equations in brainly.com/question/4326955
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In this attached picture according to the conditions of the problem we have an isosceles trapezoid and since we know that legs are equal (AD=BC=5 cm), we have to calculate bases and height in order to find the area. Working with the triangle BCD, we apply Pythagoras theorem and find that CD = = 10 cm. Since BDC is a right triangle, applying theorem for the area of triangles, we find that
and BF=
. Since ABCD is an isosceles trapezoid, triangles ADE and BFC are congruent with Angle Side Angle theorem. Then, DE=FC and with the help of Pythagoras theorem, DE=FC=2.5 cm. Then, AB=EF=5 cm and the area of the trapezoid is
