Find the equation of the line that contains the point (21,27) and is parallel to the x-axis.

Elodia [21]

Hi, I'm happy to help!

To find the slope, you need to use the slope formula, where m is the slope:

m= $\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }$

Slope means rise over run, or how much the line rises per the amount the line moves forward. This equation shows the movement from the y points to show rise, over the difference in the x points to show run.

Now, to find the slope we insert our values, starting with our second y point:

m= $\frac{2-y_{1 } }{x_{2} -x_{1} }$

Now insert our first y point:

m= $\frac{2-4 }{x_{2} -x_{1} }$

Now we insert our second x point:

m= $\frac{2-4 }{-3 -x_{1} }$

And finally our first x point:

m= $\frac{2-4 }{-3 -3 }$

Now, we solve:

m= $\frac{-2 }{-6}$

So, our slope is -2/-6, to simplify it, we remove both negatives because they cancel each other out.

m= $\frac{2 }{6}$

Now, we simplify our fraction by dividing the top and bottom by 2:

m= $\frac{1}{3}$

So, our slope is 1/3. This means that for every 1 unit the line rises, it goes to the right 3 units. The y-intercept is where the line hits the y axis.

If the question is asking for slope intercept form for the equation, you use y=mx+b

y represents any y coordinate on your line, m represents your slope (1/3), x represents any x coordinate on your line, and b represents your y-intercept (3).

If you were to insert these values, you would get:

y= $\frac{1}{3}$ x+3

You use this to find what a y coordinate would be so you can draw your line.

For the next equation we do the same thing:

m= $\frac{y_{2}-y_{1 } }{x_{2} -x_{1} }$

Insert our values:

m= $\frac{4-1}{2-(-4)}$

Get rid of the double negative:

m= $\frac{4-1}{2+4}$

Solve:

m= $\frac{3}{6}$

Simplify:

m= $\frac{1}{2}$

Now that we know our slope, let's plug it in to our slope intercept form equation.

y= $\frac{1}{2}$ x+3

I hope this was helpful! Keep learning! :D

5 0

2 years ago

Please help me and if I can I’ll help you but please I don’t get it!!

kobusy [5.1K]

Step-by-step explanation:

To solve this problem, let's set up our equation to solve for x (time to travel 13 miles).

$\frac{65}{1} =\frac{13}{x}$

We use this equation to find x. To solve, we divide 13 by 65 to get our answer.

13 ÷ 65 = 0.2

Our answer: 0.2 hours

4 0

2 years ago

-3(-2x+1)-x=3(-x+2)-1

olga55 [171]

Answer: I think it is 5 or 4

8 0

2 years ago

Read 2 more answers

Help me with 8-9 if you get it right i would give you brain list have a good day!

ad-work [718]

Answer:

i cant help with that cause i have no way of drawing

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

A survey found 195 of 250 randomly selected Internet users have high-speed Internet access at home. Construct a 90% confidence i

Andrej [43]

Answer:

d. (0.737, 0.823)

The 90% confidence interval is = (0.737, 0.823)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

p+/-z√(p(1-p)/n)

Given that;

Proportion p = 195/250 = 0.78

Number of samples n = 250

Confidence interval = 90%

z value(at 90% confidence) = 1.645

Substituting the values we have;

0.78 +/- 1.645√(0.78(1-0.78)/250)

0.78 +/- 1.645√(0.0006864)

0.78 +/- 1.645(0.026199236630)

0.78 +/- 0.043097744256

0.78 +/- 0.043

(0.737, 0.823)

The 90% confidence interval is = (0.737, 0.823)

8 0

2 years ago