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marta [7]
2 years ago
6

Find an equation of the line through (3,5) and parallel to y = 3x -7. Write the equation using function notation

Mathematics
1 answer:
ki77a [65]2 years ago
7 0

Given:

Equation of line is y=3x-7.

To find:

The equation of line which is parallel line to y=3x-7 and passes through (3,5) in function notation.

Solution:

Slope intercept form of a line is

y=mx+b

where, m is slope and b is y-intercept.

On comparing the equation y=3x-7 with slope intercept form, we get

m=3

So, slope of given line is 3.

Slope of parallel lines are same. Thus, the slope of parallel line is also 3.

Point slope form of a line is

y-y_1=m(x-x_1)

where, m is slope.

The parallel line passes through (3,5) with slope 3. So, the equation of line is

y-5=3(x-3)

y-5=3x-9

Add 5 on both sides.

y=3x-9+5

y=3x-4

Function notation of this equation is

f(x)=3x-4

Therefore, the equation equation in function notation is f(x)=3x-4.

You might be interested in
Alliic
pochemuha
First, we need to solve the first equation in order to see what the options need to be equivalent to. our first step to solving this is to distribute -3 through the parenthesis 
y + 5 = -3x + 3
next, move the constant to the right side and change its sign
y = -3x + 3 - 5
calculate the difference
y = -3x - 2
since we cant find x, your final solution for y is y = -3x - 2, x ∈ R
now that we know the solution to that equation, we can now solve the options listed to see which ones are equivalent.
first is y = -3x - 2, which is very simple to solve because y has already been found. since we know y and there is no solution for x, our answer to this equation is y = -3x -2, x ∈ R. since this is the exact same answer as our first equation, we know that the A is equivalent to y + 5 = -3(x - 1)
the next equation is also already solved for y and has no x, so the answer to this equation is y = -4x - 5, x ∈ R. since this is does not have the same answer that <span>y + 5 = -3(x - 1) had</span>, option B is not equivalent.
our next equation is 3x + y = -2 does not provide y for us, so we must solve it.
first, you need to move the variable to the right side and change its sign
3x = -2 - y
now divide both sides of the equation by 3
x = - 2/3 = y/3
write all the numerators above their common denominators
x = - 2 + y/3 
since we dont know what y is, our final solution is
x = - \frac{2+y}{3} , y ∈ R
since this answer does not match the answer we are looking for, option C is not equivalent.  
finally, we must solve -4x + y = -5
the first step to solving this is to move the variable to the right side and change its sign
-4x = -5 - y
divide both sides of the equation by -4
x = 5/4 + y/4
now, write all the numerators above their common denominators 
x = 5 + y/4
since we dont know what y is, our answer is x = \frac{5+y}{4} , y ∈ R
since this is also not equivalent to <span>y + 5 = -3(x - 1), our only answer is option A.
let me know if you have any further questions 
:)</span>
5 0
2 years ago
I NEED HELP................................................... BRAINLIEST?
Mumz [18]

Remark

Good thing to know. This is a rounding question.

A

Answer A is a bit nasty. I round 5 to the next highest number on the left. That may not be what you have been told to do. Let us round A to  5.7 and see if anything else does this.

B

Answer B rounds to 5.6

C

Answer C rounds to 5.6 as well. 3 is less than 5 so you round down.

D

Answer D rounds to 5.6(.) The zero has no effect on the 6.

Answer

Since there is nothing special about A and nothing else rounds to 5.7, the answer is A. So your rule is when the last number is 5, you round the second last number to one more than it was, regardless of the properties of the second last number.

3 0
2 years ago
Solve each pair of simultaneous equations by substitution method
WARRIOR [948]

Answer:

x = 1       y = -4

Step-by-step explanation:

- Plug the value of y into the other equation.

x + 3y = -11

x + 3(-4x) = -11

x - 12x = -11

-11x = -11

x = 1

- Now substitute the value of x into any equation.

y = -4x

y = -4(1)

y = -4

3 0
2 years ago
Read 2 more answers
A man buys a backpack from a sporting goods
Lelechka [254]

Answer:

He would pay a total of $21.50

Step-by-step explanation:

A trick that I learned is to take the zeros and decimals off. Then multiply. Ex) 75 × 2 =150. Take away the zero (15) and ad the decimal (1.5)

I'm not the best at explaining but I hope this helps

8 0
2 years ago
12 is what percent of 10
Delicious77 [7]
Your answer is 1.2.


I hope I helped you! :)
5 0
3 years ago
Read 2 more answers
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