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fomenos
2 years ago
13

The y-intercept of the line which contains the following points (-8-35) and (6,21)

Mathematics
1 answer:
AlladinOne [14]2 years ago
3 0

Answer:

The answer to your question is -3

Step-by-step explanation:

Data

A (-8, -35)

B (6, 21)

Process

1.- Calculate the slope

slope = m = (y2 - y1) / (x2 - x1)

x1 = -8  y1 = -35   x2 = 6   y2 = 21

-Substitution

            m = (21 + 35) / (6 + 8)

-Simplification

            m = 56 / 14

-Result

            m = 4

2.- Calculate the equation of the line

            y - y1 = m(x - x1)

-Substitution

            y + 35 = 4(x + 8)

-Simplification

            y + 35 = 4x + 32

            y = 4x + 32 - 35

-Result

             y = 4x - 3

3.- Find the y-intercept

The y-intercept is the number after the x, for this equation is -3.

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F(x) = x^2. What is g(x)
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Answer:

g(x) = - x² - 4 ⇒ A

Step-by-step explanation:

Let us revise the reflection and translation of a function

  • If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
  • If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
  • If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)  
  • If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)  
  • If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k  
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f(x) = x² is the blue curve

g(x) is its image is the red curve

∵ g(x) is the image of f(x)

∵ f(x) is opened upward

∵ g(x) is opened downward

→ That means the sign of y-coordinates of all points on the blue

   graph are opposite

∴ f(x) is reflected about the x-axis

∴ Its image is - f(x)

∵ The vertex of f(x) is (0, 0)

∵ The vertex of g(x) = (0, -4)

→ That means the function translated 4 units down

∴ - f(x) is translated 4 units down

∴ Its image is - f(x) - 4

∴ g(x) = - f(x) - 4

∵ f(x) = x²

∴ g(x) = - x² - 4

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