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allsm [11]
3 years ago
9

Write the equation of a linear function f, such that f(1)=4 and f(4)=1 Then find f(-2)

Mathematics
1 answer:
trapecia [35]3 years ago
7 0

If <em>f(x)</em> is a linear function, then

<em>f(x)</em> = <em>ax</em> + <em>b</em>

for some constants <em>a</em> and <em>b</em>.

Given that <em>f</em> (1) = 4 and <em>f</em> (4) = 1, these constants are such that

<em>f</em> (1) = <em>a</em> + <em>b</em> = 4

<em>f</em> (4) = 4<em>a</em> + <em>b</em> = 1

Solve for <em>a</em> and <em>b</em> : eliminate <em>b</em> by subtracting the two equations,

(<em>a</em> + <em>b</em>) - (4<em>a</em> + <em>b</em>) = 4 - 1

-3<em>a</em> = 3

<em>a</em> = -1

Then

-1 + <em>b</em> = 4

<em>b</em> = 5

So we have

<em>f(x)</em> = -<em>x</em> + 5

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Answer:

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y=x: has a negative slope.

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Look at the picture.

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A 30 Oz box of Lucky Charms cost $4.50 a 20 oz box cost $3.60 what is the unit price of each box
notka56 [123]

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3 years ago
Determine the equation of the line given by the graph.
PolarNik [594]

Hello!

I was going to try to use the slope formula, and solve for the y-intercept, but the given graph is hard to distinguish accurate ordered pairs. So, we will find the equation with the graph instead.

Looking at the graph, we can see that the y-intercept is negative. Also, we can also determine that each square represents one unit. So, the y-intercept has to be -3/2 or -1.5. That removes the choices A and C because the y-intercept is in between the values of -1 and -2.

Secondly, the graph has a positive slope. Why? When the x-values increase, the y-values increase. Also, when the x-values decrease, the y-values also decrease. This tells us that the graph has a positive slope (this doesn't remove any choices, but it helps to distinguish which graph has a positive or negative slope).

Finally, we know that if the slope is greater than one, then it is steeper (m > 1). But, if it's less than one, then it becomes less steep (0 < m < 1). Looking at the graph, the graph looks relatively steep (graphing the equations y = 5/7 x - 3/2 and y = 7/5x - 3/2 can help you see the differences between them).

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3 0
4 years ago
Answer correct for brainliest and also get a thanks !
zaharov [31]
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am I correct? Fix my answer if I am not.
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