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3 years ago

Find the equation of a line that is parallel to y = 2x + 3 and passes through (-1, -1).

Mathematics

1 answer:

drek231 [11]3 years ago

4 0

Answer:

y = 2x +1

Step-by-step explanation:

The given line is in "slope-intercept" form, where the slope is the coefficient of x, 2, and the intercept is the added constant, 3. The parallel line will have the same slope, but its constant will be different. We can find the constant by putting the given point into an equation with the constant as the unknown:

y = 2x + b

-1 = 2(-1) +b . . . substitute for x and y

2 -1 = b . . . . . . add 2

1 = b

So the equation for the parallel line is ...

y = 2x + 1

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Tell whether the data in the table can be modeled by a linear equation. Explain.

anastassius [24]

Answer:

y = -3x + 7

Step-by-step explanation:

Choosing two points from the given table:

Let (x1, y1) = (-3, 16)

(x2, y2) = (-1, 10)

Plug these given values into the slope formula:

m = (y2 - y1)/(x2 - x1)

= (10 - 16) / (-1 - (-3))

= -6 / (-1 + 3)

= -6/2

= -3

Therefore, the slope is -3.

Next, choose one of the points and plug into the <u>point-slope form</u>:

Let's use (-1, 10) as (x1, y1):

y - y1 = m(x - x1)

y - 10 = -3(x - (-1))

y - 10 = -3(x + 1)

y - 10 = -3x - 3

Add 10 on both sides to isolate y:

y - 10 + 10 = -3x - 3 + 10

y = -3x + 7

8 0

2 years ago

Please help, will give brainliest to correct answer.

Harrizon [31]

The answer is f(x)=16(1/4)^x

7 0

3 years ago

In a class of 6, there are 2 students who forgot their lunch.

lukranit [14]

Answer:

1/8

Step-by-step explanation:

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4 0

3 years ago

Prove for any positive integer n, n^3 +11n is a multiple of 6

suter [353]

There are probably other ways to approach this, but I'll focus on a proof by induction.

The base case is that n = 1. Plugging this into the expression gets us

n^3+11n = 1^3+11(1) = 1+11 = 12

which is a multiple of 6. So that takes care of the base case.

----------------------------------

Now for the inductive step, which is often a tricky thing to grasp if you're not used to it. I recommend keeping at practice to get better familiar with these types of proofs.

The idea is this: assume that k^3+11k is a multiple of 6 for some integer k > 1

Based on that assumption, we need to prove that (k+1)^3+11(k+1) is also a multiple of 6. Note how I've replaced every k with k+1. This is the next value up after k.

If we can show that the (k+1)th case works, based on the assumption, then we've effectively wrapped up the inductive proof. Think of it like a chain of dominoes. One knocks over the other to take care of every case (aka every positive integer n)

-----------------------------------

Let's do a bit of algebra to say

(k+1)^3+11(k+1)

(k^3+3k^2+3k+1) + 11(k+1)

k^3+3k^2+3k+1+11k+11

(k^3+11k) + (3k^2+3k+12)

(k^3+11k) + 3(k^2+k+4)

At this point, we have the k^3+11k as the first group while we have 3(k^2+k+4) as the second group. We already know that k^3+11k is a multiple of 6, so we don't need to worry about it. We just need to show that 3(k^2+k+4) is also a multiple of 6. This means we need to show k^2+k+4 is a multiple of 2, i.e. it's even.

------------------------------------

If k is even, then k = 2m for some integer m

That means k^2+k+4 = (2m)^2+(2m)+4 = 4m^2+2m+4 = 2(m^2+m+2)

We can see that if k is even, then k^2+k+4 is also even.

If k is odd, then k = 2m+1 and

k^2+k+4 = (2m+1)^2+(2m+1)+4 = 4m^2+4m+1+2m+1+4 = 2(2m^2+3m+3)

That shows k^2+k+4 is even when k is odd.

-------------------------------------

In short, the last section shows that k^2+k+4 is always even for any integer

That then points to 3(k^2+k+4) being a multiple of 6

Which then further points to (k^3+11k) + 3(k^2+k+4) being a multiple of 6

It's a lot of work, but we've shown that (k+1)^3+11(k+1) is a multiple of 6 based on the assumption that k^3+11k is a multiple of 6.

This concludes the inductive step and overall the proof is done by this point.

6 0

3 years ago

Read 2 more answers

I need help to these questions. Convert these fractions to a decimal 7/8 , 4 3/8. Thanks

ehidna [41]

Simple...

you have: $\frac{7}{8}$ and $4 \frac{3}{8}$

Now, the first one is easy just divide it...

$\frac{7}{8} =0.875$

Now....

$4 \frac{3}{8}$ needs to be converted...

Multiply the whole number*denominator...

4*8=32

Now add the numerator....

32+3=35

Now use the original denominator...

$\frac{35}{8}$

Now divide...

$\frac{35}{8}=4.375
$

Thus, your answer.

7 0

3 years ago

Read 2 more answers