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joja [24]
2 years ago
12

HELP!! 15 POINTS

Mathematics
2 answers:
forsale [732]2 years ago
8 0

Answer:

1. y varies directly with x and the equation is  y=1.375x

2. No, y does not vary directly with x

3. Your car travels 58 miles in 1 hour

4. -\frac{1}{3}

4. -3

5. -\frac{26}{27}

6. y-2=3(x-5)

7. y+5=-\frac{2}{5}(x+3)

8. y+7=-0.54(x-4)

9. y-16=8(x-2)

10. 2x+3y=21

11. x+2y=2


Step-by-step explanation:


1.

<em>For y to vary directly with x , all the 3 pair of numbers need to show the same ratio if we divide each y's by the x's</em>. Let's check.

  • \frac{11}{8}=1.375
  • \frac{22}{16}=1.375
  • \frac{33}{24}=1.375

So all of them show the same ratio and hence y varies directly with x.

<em>For equation, we already saw that multiplying x by 1.375 gives us y.</em> We can write in equation form as:

y=1.375x

Third answer choice is correct.


2.

This is similar to #1. So let's check the ratios.

  • \frac{4}{16}=0.25
  • \frac{16}{32}=0.5
  • \frac{36}{48}=0.75

As we can see, the ratios are not equal to y does not vary directly with x.

Fourth answer choice is correct.


3.

<em>The first number in the pair gives time and second number gives distance. To get unit rate, we divide the distance by time. S</em><em>o we will get the number of miles traveled in 1 hour.</em>

\frac{233}{4}=58.25  <u>[ i believe this is a typo and it should be 232 miles and ratio would be 58 ]</u>

<u>\frac{348}{6}=58</u>

<u>\frac{464}{8}=58</u>

<u>\frac{580}{10}=58</u>

As we can see, in 1 hour, distance covered is 58 miles. Third answer choice is right.


4.

If the 2 points are taken as  (x_{1},y_{1})  and  (x_{2},y_{2})

And we know formula of slope to be:

\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

The slope of the line is:

\frac{3-5}{8-2}=\frac{-2}{6}=-\frac{1}{3}

The slope of the line is  -\frac{1}{3}

Second answer choice is correct.


4. [this should be #5]

If the 2 points are taken as  (x_{1},y_{1})  and  (x_{2},y_{2})

And we know formula of slope to be:

\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

The slope of this line can be found now:

\frac{2.7-8.7}{-3.2-(-5.2)}=\frac{2.7-8.7}{-3.2+5.2}=\frac{-6}{2}=-3

The slope of the line is  -3

Fourth answer choice is correct.


5.

The formula of slope is:

\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

Where,

the 2 points are taken as  (x_{1},y_{1})  and  (x_{2},y_{2})

Now finding the slope:

\frac{\frac{7}{3}-(-2)}{-3-\frac{3}{2}}=\frac{\frac{7}{3}+2}{-\frac{9}{2}}=\frac{\frac{13}{3}}{-\frac{9}{2}}=-\frac{26}{27}

The slope of the line is  -\frac{26}{27}

Second answer choice is right.


6.

Point Slope form of a line is given as:

y-y_{1}=m(x-x_{1})

Where,

  • (x_{1},y_{1}) is the point given, and
  • m is the slope

Using the point (5, 2) and slope as 3 given, we can write the equation:

y-2=3(x-5)

Fourth answer choice is right.


7.

Point Slope form of a line is given as:

y-y_{1}=m(x-x_{1})

Where,

  • (x_{1},y_{1}) is the point given, and
  • m is the slope

Using the point given as  (-3,-5) and slope as m=-\frac{2}{5} , we can write the point slope form of the equation as:

y-(-5)=-\frac{2}{5}(x-(-3))\\y+5=-\frac{2}{5}(x+3)

First answer choice is right.


8.

Point Slope form of a line is given as:

y-y_{1}=m(x-x_{1})

Where,

  • (x_{1},y_{1}) is the point given, and
  • m is the slope

The slope is given as -0.54 and the point is (4, -7). So the point slope form is:

y-(-7)=-0.54(x-4)\\y+7=-0.54(x-4)

First answer choice is right.


9.

In this question, we can just have a quick look and see that the y-coordinate is 8 times the x-coordinate. <em>So we can say that y=8x </em>

<u>Expanding the equations below would tell us which one is equal to that. Let's check.</u>

y-16=8(x-2)\\y-16=8x-16\\y=8x-16+16\\y=8x

This is the correct one.

So first answer choice is right.


10.

The standard form of the equation of a line is given as:

Ax+By=C

Rearranging the given equation gives us:

y=-\frac{2}{3}x+7\\\frac{2}{3}x+y=7

<em>Now, we can't have a fraction, so we multiply all of it by 3 to get rid of the denominator. Now we have:</em>

3*(\frac{2}{3}x+y=7)\\2x+3y=21

First answer choice is right.


11.

The standard form of a line is  Ax+By=C

Rearranging the given equation, we have:

y=-\frac{1}{2}x+1\\\frac{1}{2}x+y=1

<em>We cannot have fractions, so we multiply the whole thing by 2 to get rid of the denominator. So we have:</em>

2*(\frac{1}{2}x+y=1)\\x+2y=2

First answer choice is correct.







Sladkaya [172]2 years ago
3 0
<span>1. For the data in the table, does y vary directly with X? If it does write an equation for the direct variation.(X,y) (8,11) (16,22) (24,33) 
</span><span>
Yes y=1.375x 

</span><span>2.for the data in the table, does y vary directly with X? If it does write an equation for the direct variation. (X,y) (16,4) (32,16) (48,36) 
</span>No y does not very directly with x*** <span> 

</span><span>3. (Time/hour,distance/miles)(4,233) (6,348) (8,464) (10, 580) 
Express the relationship between distance and time in a simplified form as a unit rate. Determine which statement correctly interprets this relationship. 
</span><span>58/1 your car travels 58 miles in 1 hour 

</span><span>4.what is the slope of the line that passes through the pair of points (2,5) and (8,3) 

</span>-1/3 

<span>4.what is the slope of the line that passes through the pair of points (-5.2,8.7) and (-3.2,2.7) 
</span>
-3 

<span>5. What is the slope of the line that passes through the pair of points (3/2,-2) and (-3,7/3) 

-26/27 

</span><span>6.write an equation in point slope from for the line through the given point with the given slope (5,2) m=3 
 
Y-2=3(X-5) 


7. Write an equation in point slope form for the line through the given point with the given slope (-3,-5) m=-2/5 

Y+5=-2/5(X+3) 

</span><span>8. Write an equation in point slope from for the line through the given point with the given slope. (4,-7) m=-0.54 

Y+7=-0.54(x-4) 

9. The table shows the height of a plant as it grows. Which equation in point slope from gives the plants height (time,plant height) (2,16)(4,32)(6,48)(8,64) 

Y-16=8(X-2)*** 
</span>
<span>10. Write y=-2/3x+7 in standard form

2x+3y=21 



11. Write y=-1/2x+1 in standard form using integers 

X+2y=2 

</span>
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