Pretty please help guys!!

Answers

Answer 1

Answer: For #1:

y = x + 4

Parallel lines have the SAME slope, this equation is in the form of y = mx + b, where 'm' is the slope. So the slope here is 1.

To find the equation of a line that passes through (2, 2) and has a slope of 1, we can plug it into point-slope form:

y - y1 = m(x - x1)

Where 'y1' is the y-value of the point, 'x1' is the x-value of the point, and 'm' is the slope.

y - 2 = 1(x - 2)

Distribute 1 into the parenthesis:

y - 2 = x - 2

Add 2 to both sides:

y = x

So your equation is y = x.

Answer 2

Answer:
IGreen's answer is elegant and totally correct, but I'm guessing that you'll get
confused when you try to dig through it. Allow me to present a simpler method,
if I may:

-- In your picture, we can only see 1, 3, and 5. We can't see enough of 2, 4,
or 6 to work on them.
But ALL six of the problems on this page are examples of the same thing:
Write the equation of a line when you know the slope and one point on the
line. That's it !

Rules to use:

-- The slope-intercept form of the equation of a line is

   y = (slope) x + (intercept)

-- When two lines are parallel, they have the SAME slope.

-- When two lines are perpendicular, their slopes are negative reciprocals.
. . . . . 'negative' means the opposite sign
. . . . . 'reciprocal' means flip a fraction over, or take 1 / (a whole number).
negative reciprocal of 3/4 is (- 4/3)
negative reciprocal of -2 is (+ 1/2)
etc.

And now you're ready to solve all six problems.

#1). through (2,2) and parallel to [ y = x + 4 ] .

"parallel" means the new line has the same slope as [ y = x + 4 ] .
What is the slope of [ y = x + 4 ] ? It's the '1' that's not written next to 'x'.
So the new line is going to be [ y = 1x + b ].
All you need to find is 'b'.

Whatever equation you find for the new line, it'll be true for every point on
the line.
You already know one point on the new line ... (2,2) ... The equation must be
true for this point. Write this point into the new equation:

   y = 1x + b

   2 = 1(2) + b

   2 = 2 + b

What is 'b' ? Subtract 2 from each side, and you have

   0 = b .

So the equation of the new line is [ y = x + 0 ] or just [ y = x ].

That's how to do them when the new line is parallel to a given line.
Now do one where the new line is perpendicular to a given line.

#5). through (1, -5) and perpendicular to [ y = -1/8 x + 2 ].

What's the slope of the new line ? In order to be perpendicular to this one,
the slope of the new one must be the negative reciprocal of -1/8 .
The negative of -(anything) is +.
The reciprocal of 1/8 is 8 .
So the slope of the new line is +8 .
The equation of the new line is . . . [ y = 8x + b ].
How to find 'b' ?
Take the point you know on the new line (1, -5), and write it into this equation:

   -5 = 8(1) + b

Squeeze 'b' out of this, and you have the equation of your new line.

All of the other problems on the page are just like these. All together,
on the whole page, there are 4 problems where the new line is parallel
to the given line, and two problems where the new line is perpendicular
to the given one. You should be able to whip out all six in about 15 minutes.

Good luck.

Related Questions

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I sell cookies for $3 and muffins for $7. Yesterday, I made $129. I sold a total of 27 items. How many of each did I sell?
4(1-3n)-14> 4(2n+3)-9n
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Need the answers quick

Roberta has a balance of $4350 on a credit card with an APR of 30.2% paying off her balance in which of these lengths of time will result in her paying the least amount of interest?

Answers

Answer:

8 months

Step-by-step explanation:

yurrr

Margarita is hired by an accounting firm at a salary of $60,000 per year. Three years later her annual salary has increased to $70,500. Assume her salary increase linearly. Find an equation that relates her annual salary S and the number of years t that she has worked for the firm.

Answers

the salary was increased each by 10,500 dollars a year

How would I rewrite this?

Answers

Answer:

-The answer is $y^2$ .

Step-by-step explanation:

When you divide numbers/variables with exponents, the exponents will subtract each other:

$(y^5)/(y^3) =y^2$

Solve for x:

2+x=8-x

Answers

2+x=8-x

add x to each side to get all the x's on one side

2+x+x = 8-x+x

2 + 2x = 8

now subtract 2 from each side to get all the numbers on the other side

2 + 2x -2 = 8-2

2x = 6

divide by 2 on each side to get x alone

2x/2 = 6/2

x=3

Answer: x=3

Answer:x=3 I hope this helps you

Step-by-step explanation:

2+x=8-x

Move the variable to the left-hand side and change its sign like this

2+x+x=8

then do this

Move the constant to the right-hand side and change its sign like this

x+x=8-2

then do this

Collect like terms

Like this

2x=8-2

Subtract the numbers
2x=6

then do this

Divide both sides of the equation by 2 and you will get your answer

X=3

On an uphill hike Ted climbs at 3mph. Going back down, he runs at 5mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike? if possible, I would like a clear equation.

Answers

Answer:

He hiked 10 miles.

Step-by-step explanation:

rate x time = distance

The distance up and the distance down are equal

3 mi/1 hr x (h hours + 2/3 hr) = 5 mi/1 hr x h hours

3h + 2 = 5h

2 = 2h

h = 1 hour

3mi/hr x 1 2/3 hr = 5 miles

5 mi/hr x 1 hr = 5 miles

1/x-1 - 3/x+2 = 1/4

solve to find x

Answers

$(1)/(x-1)-(3)/(x+2)=(1)/(4)\n \n (x+2-3(x-1))/((x-1)(x+2))=(1)/(4)\n \n (x+2-3x+3)/((x-1)(x+2))=(1)/(4)\n \n (5-2x)/(x^2+x-2)=(1)/(4)\n \n 4(5-2x)=x^2+x-2\n \n 20-8x=x^2+x-2\n \n \boxed{x^2+9x-22=0}$

Solvin this quadratic equation with Bhaskara formula we find:

x = -11 or x = 2

$(1)/(x-1) - (3)/(x+2) = (1)/(4) \ /\cdot 4(x-1)(x+2)\n\n(4(x-1)(x+2))/(x-1) - (3\cdot 4(x-1)(x+2))/(x+2) = (4(x-1)(x+2))/(4)\n\n4(x+2)-12(x-1)=(x-1)(x+2)\n\n4x+8-12x+12=x^2+2x-x-2\n\n-8x+20=x^2+x-2\n\n-x^2-9x+22=0\ /\cdot(-1)\n\nx^2+9x-22=0\ \ \ \Rightarrow\ \ \ x^2+11x-2x-22=0\n\nx(x+11)-2(x+11)=0\n\n(x+11)(x-2)=0\ \ \ \ \ \Leftrightarrow\ \ \ (x+11=0\ \ \ or\ \ \ x-2=0)\n\nx=-11\ \ \ or\ \ \ x=2$

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