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frez [133]
2 years ago
7

83. For what value of K will the points (1, 4), (-3, 16) and (k, -2) lie on one straight line.​

Mathematics
2 answers:
lutik1710 [3]2 years ago
6 0

Answer:

I don't know

Step-by-step explanation:

I don't know

Ede4ka [16]2 years ago
6 0

Answer:

k = 3

Step-by-step explanation:

If the points lie on the same line then the slope between the points will be equal.

Calculate the slope m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (- 3, 16)

m = \frac{16-4}{-3-1} = \frac{12}{-4} = - 3

Repeat the process and equate to - 3

with (x₁, y₁ ) = (1,4) and (x₂, y₂ ) = (k, - 2)

m = \frac{-2-4}{k-1} = \frac{-6}{k-1} , then

\frac{-6}{k-1} = - 3 ( multiply both sides by k - 1 )

- 6 = - 3(k - 1) ← divide both sides by - 3

2 = k - 1 ( add 1 to both sides )

3 = k

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PLEASE HELP!!! BRAINLIEST TO CORRECT COMPLETE ANSWER!
notka56 [123]

Answer:

y=16x+1

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(1,17) and (2,33).

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y = mx+b

Where:

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First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (1,17), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=1 and y1=17.

Also, let's call the second point you gave, (2,33), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=2 and y2=33.

Now, just plug the numbers into the formula for m above, like this:

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or...

m=  16/ 1

or...

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(2,33). When x of the line is 2, y of the line must be 33.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=16x+b. b is what we want, the 16 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (1,17) and (2,33).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(1,17). y=mx+b or 17=16 × 1+b, or solving for b: b=17-(16)(1). b=1.

(2,33). y=mx+b or 33=16 × 2+b, or solving for b: b=33-(16)(2). b=1.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(1,17) and (2,33)  is   y=16x+1

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