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3 years ago

Given the point (1, 3) and a slope of 2, write an equation in point-slope form.

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

6 0

Answer:

y=2x+1

Step-by-step explanation:

Since we are given a point and a slope, we can use the point slope formula

$y-y_{1} =m(x-x_{1})$

m is the slope. In this case, m is 2.

y1 is the y coordinate of the point given. y1 is 3.

x1 is the x coordinate of the point given. x1 is 1

y-3=2(x-1)

Now, we need to get the equation into point slope form: y=mx+b

To do this, we need to get y by itself

First, distribute the 2 on the right

y-3=2*x+ 2*-1

y-3=2x-2

Add 3 to both sides

y-3+3=2x-2+3

y=2x+1

The equation is in y=mx+b form, so our final equation is:

y=2x+1

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The relation {(-1 , 3), (4 , 2), (-1 , 5)} is not a function ⇒ 2nd

Step-by-step explanation:

Let us revise the meaning of relation and function

The relation is a set of inputs and outputs
A function is a relation with one output for each input, that means every x has only one y
Ex: {(2 , 3) , (-1 , -2) , (3 , 2)} is a function because 2 has only 3 , -1 has only -2 and 3 has only 2, {(1 , 7) , (2 , -4) , (1 , -3)} is not a function because 1 has 7 and -3

The relation is a function if and only if every x has only one y

In {(0 , 0), (1 , 0), (2 , 0)}

∵ x = 0 has y = 0

∵ x = 1 has y = 0

∵ x = 2 has y = 0

∴ Every x has only one y

∴ {(0 , 0), (1 , 0), (2 , 0)} is a function

In {(-1 , 3), (4 , 2), (-1 , 5)}

∵ x = -1 has y = 3

∵ x = 4 has y = 2

∵ x = -1 has y = 5

∴ x = -1 has y = 3 and 5

∴ Not every x has only one y

∴ {(-1 , 3), (4 , 2), (-1 , 5)} is not a function

In {(1 , 2), (3 , -5), (-1 , 7)}

∵ x = 1 has y = 2

∵ x = 3 has y = -5

∵ x = -1 has y = 7

∴ Every x has only one y

∴ {(1 , 2), (3 , -5), (-1 , 7)} is a function

In {(7 , -1), (3 , -2), (5 , -2)}

∵ x = 7 has y = -1

∵ x = 3 has y = -2

∵ x = 5 has y = -2

∴ Every x has only one y

∴ {(7 , -1), (3 , -2), (5 , -2)} is a function

The relation {(-1 , 3), (4 , 2), (-1 , 5)} is not a function

Learn more:

You can learn more about the relations and functions in brainly.com/question/10570041

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A man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. He puts twice as muc

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Let x represent amount invested in the higher-yielding account.

We have been given that a man puts twice as much in the lower-yielding account because it is less risky. So amount invested in the lower-yielding account would be $2x$ .