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-BARSIC- [3]
3 years ago
5

Find an equation of the line having the given slope and containing the given point.

Mathematics
1 answer:
saul85 [17]3 years ago
4 0

Answer:

y = 4x - 12

Step-by-step explanation:

The equation of a line has the following format:

y = mx + b

In which m is the slope and b is the y-intercept(value of x when y = 0).

In this question:

Slope 4, which means that m = 4.

So

y = 4x + b

Contains point (1,-8).

This means that when x = 1, y = -8. We replace this into the equation to find b. So

y = 4x + b

-8 = 4(1) + b

b = -12

So

y = 4x - 12

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What is the range of the function graphed below?
aleksandrvk [35]

Answer:       B.     [–4, 0)  ∪  [2, ∞)

To find the range, find out what y-values are possible for the function in the graph.

<h2>Symbols</h2>

We need to pay attention to what symbols to use.

<h3>Reading the diagram</h3>

Solid circle

  • The function touches the point.

Empty circle

  • The function gets close, but does not touch the point.

Arrow

  • The function keeps going to infinity.

<h3>Writing range in set notation</h3>

Square brackets: [ and ]

  • These show that the function touches the point.

Curved brackets: ( and )

  • These show that the function gets close but does not touch the point.
  • Infinity always uses a curved bracket.

Union of sets: ∪

  • This symbol shows that sets of values are talking about the same thing. It's almost like the word 'and'.

<h2>Finding the range of the graphed function</h2><h3>Lower blue line</h3>

Let's start by looking for the lowest possible y-value at the bottom of the diagram. On the graph, the point (4, –4) marked with a solid circle.

The function touches the point and stops. Since the y-value is –4, the lowest possible y-value is:     -4

If we follow the blue line upwards, we find an empty circle at (0, 0). The y-value in (0, 0) is 0. This means that the function gets close, but does not include:     0

So, the first part of our range is:

  • [–4, 0)

<h3>Upper blue line</h3>

The blue line on the top starts where y = 2 at a solid circle. So, the function includes the y-value:    2

If we follow this blue line upwards, it ends with an arrow. This means it will keep going to infinity, which is the symbol:    \infty

So, the second part of our range is:

  • [2, ∞)

<h2>Putting it together</h2>

Put the lower and upper blue lines together with the union of sets symbol. The range is expressed as:    [–4, 0)  ∪  [2, ∞)

Learn more about domain and range here:

brainly.com/question/20349151

4 0
2 years ago
Jake earned $400 over the summer. He earned $220 mowing lawns, and he earned the rest washing cars for $10 each. He used this eq
vlada-n [284]
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8 0
3 years ago
Can u plz help me with this
7nadin3 [17]

Answer:

x = 61, y = 29

Step-by-step explanation:

29+x = 90

x = 61

x + y = 90

y + 61 = 90

y = 29

8 0
2 years ago
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A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 93 m
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Write the point-slope form of the equation of the line with a slope of - 2 and an x-intercept of - 1. Include your work in your
coldgirl [10]
X-intercept is -1 implies line passes through (-1,0). 
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y - 0 = -2 (x -(-1) )

>> y  = -2 (x +1)   <----- FINAL ANSWER
8 0
3 years ago
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