All categories

3 years ago

Write the equation of the line that passes through points (-4, 5) and (0,13) in slope-intercept form.

Mathematics

1 answer:

LiRa [457]3 years ago

8 0

Answer:

The answer is

$y = 2x + 13$

Step-by-step explanation:

Remember:

$Slope-intercept form: \: \\ y = mx + b \\ \\ m = slope \\ b = y - intercept$

$M = \frac{y_2 - y_1}{x_2 - x_1}$

First: Find the slope.

$M = \frac{13 - 5}{0 - ( - 4)} = \frac{8}{4} = 2$

Second: Solve for the y-intercept

$y = mx + b \\ 5 = 2( - 4) + b \\ 5 = - 8 + b \\ \frac{+ 8 = + 8 \: \: \: \: \: \: \: \: }{13 = b}$

Third: Plug in.

$y = mx + b \\ y = 2x + 13$

You might be interested in

I need help please and thank you

ExtremeBDS [4]

Answer:

D=340

Step-by-step explanation:

360-180/9

360-20

340

4 0

3 years ago

Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work together, it takes them 2 hours. How

aalyn [17]

Answer:

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood = K hrs

So, the per hour rate of Dwight = $(\frac{1}{K})$

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood = (K- 3) hrs

So, the per hour rate of Joe = $(\frac{1}{K-3})$

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them = $(\frac{1}{2})$

⇒ Per hour rate of ( Dwight + Joe) = $(\frac{1}{2} )$

$\implies (\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})$

Now, solving for the value of K , we get:

$(\frac{1}{K}) + (\frac{1}{K-3}) = (\frac{1}{2})\\\implies \frac{(K-3) + K}{K (K-3)} = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K + 6= 0\\\implies K^2 - 6K - K + 6= 0\\\implies K(K-6) -1(K - 6)= 0\\\implies (K-6)(K-1) = 0$

Implies either K = 6 Or K = 1

But if K = 1, (K-3) = 1- 3 = -2 hours would be A CONTRADICTION.

⇒ K = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

8 0

3 years ago

Find two consecutive even integers whose product is 288

Trava [24]

So I’m going to solve this using algebra OK?
So what you do is take the first integer as X.
Then we know that x(the first number) + X+2(the second number) is 288 right?
So we solve that saying x+x+2=288.
So 2X+2=288
2X+2-2=288-2 right?
So 2X=286.
So x is 286/2 right?
So x is 143.
Now the first number is 143 right?
So the second number should be 143+2 so 145.
I know they are not even but these are the solutions.
I don’t think there are any consecutive even numbers that add up to 288

6 0

3 years ago

Which number sentences show how to solve the problem?

exis [7]

72 ÷ 6 = 12 and 12 × 36 = 432 and 72 × 36 = 2,592 and 2,592 ÷ 6 = 432

8 0

3 years ago

Read 2 more answers

Write 175 miles on 5 gallons as a unit rate.

Vanyuwa [196]

Answer:

35 miles per gallon.

Step-by-step explanation:

We need to simplify 175/5 into 35/1 to make it into a unit rate. So, 35 miles per gallon is the answer.

4 0

3 years ago