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Olenka [21]
2 years ago
11

Find the equation of a line that passes through the point (0,1) and has a gradient of 2.

Mathematics
1 answer:
Usimov [2.4K]2 years ago
6 0

Answer:

  • y = 2x + 1

Step-by-step explanation:

Given point (0, 1) and the slope m = 2

<u>Use point- slope form to find the equation of the line:</u>

  • y - y₁ = m(x - x₁)
  • y - 1 = 2(x - 0)
  • y - 1 = 2x
  • y = 2x + 1
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Answer:

Part 1) The graph has three (3) x-intercepts and  has one (1) y-intercept

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Part 6) x=-6

Part 7) The horizontal line y=-1 intersects the graph three times

Part 8) The value of the function for f(6) is equal to zero

Part 9) The function is increasing on the interval (-6,-2) and (8,11) and the function is decreasing on the interval (2,8)

Part 10) The function is positive on the interval (-3,6) and (10,11) and is negative on the interval (-6,-3) and (6,10)

Step-by-step explanation:

Part 1) Find the number of x-intercepts and y-intercepts of the graph

we know that

The<u> x-intercepts</u> are the values of x when the value of y (the function) is equal to zero

Look at the graph

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The<u> y-intercepts</u> are the values of y when the value of x is equal to zero

Look at the graph            

The graph has 1 y-intercept

The y-intercept is the point (0,3)

Part 2) The y value of the minimum point on the graph is?

we know that

Look at the picture

The minimum point is (-6,-3)

therefore

The y-value of the minimum point is -3

Part 3)  f(4) is equal to?

we know that

f(4) is the value of the function when the value of x is equal to 4

Look at the graph

For x=4

The value of the function is equal to y=3

therefore

f(4)=3

Part 4) f(0) is equal to?

we know that

f(0) is the value of the function when the value of x is equal to 0

Look at the graph

For x=0

The value of the function is equal to y=3

therefore

f(0)=3

Part 5) f(5) is equal to?

we know that

f(5) is the value of the function when the value of x is equal to 5

Look at the graph

For x=5

The value of the function is about y=1.5  (see the attached figure)

therefore

f(5)=1.5

Part 6) The value of x when f(x)= -3 is?

Look at the graph

we have the point (-6,-3)

when the value of f(x)=-3

the value of x is equal to x=-6

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Look at the graph

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Look at the graph

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