1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Masja [62]
3 years ago
5

What equation represents the line that passes through (-8,11) and (4,7/2)

Mathematics
2 answers:
masha68 [24]3 years ago
8 0

For this case we have that by definition, the equation of the line in slope-intersection form is given by:

y = mx + b

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have:

(x1, y1): (- 8,11)\\(x2, y2): (4,3.5)

m = \frac {y2-y1} {x2-x1} = \frac {3.5-11} {4 - (- 8)} = \frac {-7.5} {4 + 8} = \frac {-7.5} {12 } = - \frac {\frac {15} {2}} {12} = - \frac {15} {24} = - \frac {5} {8}

Thus, the equation will be given by:

y = - \frac {5} {8} x + b

We substitute a point to find "b":

11 = - \frac {5} {8} (- 8) + b\\11 = 5 + b\\b = 11-5\\b = 6

Finally:

y = - \frac {5} {8} x + 6

Answer:

y = - \frac {5} {8} x + 6

Marianna [84]3 years ago
4 0

Answer:

So our answers could be any of these depending on the form wanted*:

y=\frac{-5}{8}x+6

5x+8y=48

y-11=\frac{-5}{8}(x+8)

y-\frac{7}{2}=\frac{-5}{8}(x-4)

*There are other ways to write this equation.

Step-by-step explanation:

So we are given two points on a line: (-8,11) and (4,7/2).

We can find the slope by using the formula \frac{y_2-y_1}{x_2-x_1} \text{ where } (x_1,y_1) \text{ and } (x_2,y+2) \text{ is on the line}.

So to do this, I'm going to line up my points vertically and then subtract vertically, then put 2nd difference over 1st difference:

( 4  ,  7/2)

-(-8 ,    11)

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

12      -7.5

So the slope is -7.5/12 or -0.625 (If you type -7.5 division sign 12 in your calculator).

-0.625 as a fraction is -5/8 (just use the f<->d button to have your calculator convert your decimal to a fraction).

Anyways the equation of a line in slope-intercept form is y=mx+b where m is the slope and b is y-intercept.

We have m=-5/8 since that is the slope.

So plugging this into y=mx+b gives us y=(-5/8)x+b.

So now we need to find b. Pick one of the points given to you (just one).

Plug it into y=(-5/8)x+b and solve for b.

y=(-5/8)x   +b with (-8,11)

11=(-5/8)(-8)+b

11=5+b

11-5=b

6=b

So the equation of the line in slope-intercept form is y=(-5/8)x+6.

We can also put in standard form which is ax+by=c where a,b,c are integers.

y=(-5/8)x+6

First step: We want to get rid of the fraction by multiplying both sides by 8:

8y=-5x+48

Second step: Add 5x on both sides:

5x+8y=48 (This is standard form.)

Now you can also out the line point-slope form, y-y_1=m(x-x_1) \text{ where } m \text{ is the slope and } (x_1,y_1) \text{ is a point on the line }

So you can say either is correct:

y-11=\frac{-5}{8}(x-(-8))

or after simplifying:

y-11=\frac{-5}{8}(x+8)

Someone might have decided to use the other point; that is fine:

y-\frac{7}{2}=\frac{-5}{8}(x-4)

So our answers could be any of these depending on the form wanted*:

y=\frac{-5}{8}x+6

5x+8y=48

y-11=\frac{-5}{8}(x+8)

y-\frac{7}{2}=\frac{-5}{8}(x-4)

You might be interested in
2. Find the number of cubical
lys-0071 [83]

Answer:number of boxes = 60

Volume of box = side × side × side.

 = 3 × 3 × 3

= 27 cu. cm.

Volume of carton = length × breadth × height.

= 15 × 9 × 12

= 1620 cu. cm.

Number of boxes = Volume of carton/Volume of each box.

= 1620/27

= 60

Therefore, number of boxes = 60.

Step-by-step explanation:Volume of box = side × side × side.

 = 3 × 3 × 3

= 27 cu. cm.

Volume of carton = length × breadth × height.

= 15 × 9 × 12

= 1620 cu. cm.

Number of boxes = Volume of carton/Volume of each box.

= 1620/27

= 60

Therefore, number of boxes = 60.

3 0
3 years ago
Find the value of x (helppppppppppppoppppppp)
Anna35 [415]
X=121
.......... ... . ......
4 0
3 years ago
Lucas had a mix of red and purple jelly beans. There were 2 red jelly beans for every 3 purple jelly beans. If there are 40 jell
Alex73 [517]

Answer:

24 purple jelly beans

Step-by-step explanation:

We are told in the question that;

Lucas had a mix of red and purple jelly beans. There were 2 red jelly beans for every 3 purple jelly beans.

The results in a ratio

2:3

Where 2 represented red jelly beans

3 represented purple jelly beans

Total number of jelly beans = 40 jelly beans.

The number of purple jelly beans that we have =

3/( 2 + 3) × 40

= 3/5 × 40

= 3 × 8

= 24.

Hence, there are 24 purple jelly beans in the bag.

7 0
3 years ago
What is the common difference in this sequence: 5, 17, 29, 41, 53?
irina1246 [14]
The common difference is 12.
5 0
3 years ago
Read 2 more answers
Y+8=12 solve please
Nikitich [7]
Y=4
the answer is y=4 because you had to subtract 8 from both sides. 

7 0
3 years ago
Read 2 more answers
Other questions:
  • Find the GCF of each pair of monomials.<br><br> 24, 48m<br><br> 32a, 48b<br><br> 36k, 144km
    10·1 answer
  • Expand the following logs: <br><br> <img src="https://tex.z-dn.net/?f=log_%7B2%7D%20%5Csqrt%7Bab%5E%7B3%7D%20%7D" id="TexFormula
    9·1 answer
  • Can someone help me please. Im not sure if that answer is correct I accidentally clicked it
    12·2 answers
  • PLEASE ANSWERRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
    13·1 answer
  • Plz help me with this
    5·1 answer
  • How many points will I get if I get 60 points every 5 mins and it goes on for 4 hours?
    10·2 answers
  • Gavin is subdividing land into two plots, where one plot is in the shape of a square and the other plot is in the shape of a rec
    7·1 answer
  • WILL MARK BRAINLEST
    14·1 answer
  • Rewrite 150o in radian form.
    9·1 answer
  • A rectangular garden has an area of 6/7 square miles. If its length is 3/5 miles, what is its width?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!