The equation of line A is given by 2y − x = 6. 2 y minus x equals 6 Select the equation that could represent line B

eddy2017

eddy2017

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Hi, dear tutors. I need your guidance with this exercise

The equation of line A is given by 2y − x = 6. Select the equation that could represent line B
1645548121002.png
  1. y = –x + 3
  2. y = 3x + 8
  3. y = –2x + 7
  4. y = 0.5x + 3
I have been given an equation equal to 6 and with two variables with coefficients.
I think I have to try the answer choices, replacing y for the value given in the choices and for the value of y given in the original equation in the problem, and see if it makes it a true statement?
Is this approach correct?
Thanks in advance,
 
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First, consider the slope of graph B. You can eliminate 2 choices. Which two are left?
 
eddy2017 said:
Hi, dear tutors. I need your guidance with this exercise

The equation of line A is given by 2y − x = 6. Select the equation that could represent line B
View attachment 31251
  1. y = –x + 3
  2. y = 3x + 8
  3. y = –2x + 7
  4. y = 0.5x + 3
I have been given an equation equal to 6 and with two variables with coefficients.
I think I have to try the answer choices, replacing y for the value given in the choices and for the value of y given in the original equation in the problem, and see if it makes it a true statement?
Is this approach correct?
Thanks in advance,
Click to expand...
If I were to tackle this assignment - I would first analyze the line A and get an idea about the scale used in the axes (since it has not been shown explicitly).
When x =0 we have y = 3 and

when y = 0 we have x = -6

so for line B, as drawn

When x =0 we have y = ? and

when y = 0 we have x = ?

Now check which of those equations (including BBBs response) match your calculations, approximately.
 
The four equations given for B are in what form?

After you exclude the two equations indicated by BBB, SK's clue lets you focus on what aspect of that form?

There is a reason you were taught that form.
 
BigBeachBanana said:
First, consider the slope of graph B. You can eliminate 2 choices. Which two are left?
Click to expand...
the slope of graph b is negative so 1) and 3) are out.

JeffM said:
The four equations given for B are in what form?

After you exclude the two equations indicated by BBB, SK's clue lets you focus on what aspect of that form?

There is a reason you were taught that form.
Click to expand...
in slope intercept form
 
so, then
  1. y = –x + 3
  2. y = –2x + 7
Right, these are the ones I need. because the slope given in the original is positive
 
this is the original equation given in the problem
1645554207295.png
line B has a negative slope
so the only choice with a negative solpe is
y = –2x + 7 y
 
BigBeachBanana said:
First, consider the slope of graph B. You can eliminate 2 choices. Which two are left?
Click to expand...
rectifying: the two choices that could have been eliminated right off the bat according to the slope of the original equation is B and D
 
Subhotosh Khan said:
If I were to tackle this assignment - I would first analyze the line A and get an idea about the scale used in the axes (since it has not been shown explicitly).
When x =0 we have y = 3 and


Why do you mean by the scales used in the axes? Like the points in the x and y axis?
Click to expand...
 
Eddy, here's how I would approach the problem:
First, notice the slope of graph B is negative, so we can eliminate choices 2 and 4.
Next, I would investigate the intersecting point of the two graphs by setting the equation for line A equal to choices 1 and 3.
Now, put the given equation for line A in the form y=mx+b : [imath]2y-x=6 \implies y=\frac{6+x}{2}=3+\frac{x}{2}[/imath].
Equate line A with choice 1 and 3:
[math]\text{Choice 1:} \\3+\frac{x}{2}=-x+3 \\ \text{Choice 3:} \\3+\frac{x}{2}=-2x+7[/math]Solve for x in both choices, what do you think of the x-values? We can discuss.
 
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eddy2017 said:
the slope of the line should be the opposite of the one given in the original and that is only satisfied by
y = –2x + 7
Click to expand...
Incorrect.

Line A has a positive slope → means when x increases y increases. (refer to your drawing in post 1)

Line B has a negative slope → means when x increases y decreases. (refer to your drawing in post 1)

Out of the given choices of equations (1, 2, 3 & 4) for line B choice 1 (y = –x + 3) and choice 3 (y = –2x + 7) shows negative slope.

Do you see that.......
 
BigBeachBanana said:
Eddy, here's how I would approach the problem:
First, notice the slope of graph B is negative, so we can eliminate choices 2 and 4.
Next, I would investigate the intersecting point of the two graphs by setting the equation for line A equal to choices 1 and 3.
Now, put the given equation for line A in the form y=mx+b : [imath]2y-x=6 \implies y=\frac{6+x}{2}=3+\frac{x}{2}[/imath].
Equate line A with choice 1 and 3:
[math]\text{Choice 1:} \\3+\frac{x}{2}=-x+3 \\ \text{Choice 3:} \\3+\frac{x}{2}=-2x+7[/math]Solve for x in both choices, what do you think of the x-values? We can discuss.
Click to expand...
i'm working on it.
 
Subhotosh Khan said:
Incorrect.

Line A has a positive slope → means when x increases y increases. (refer to your drawing in post 1)

Line B has a negative slope → means when x increases y decreases. (refer to your drawing in post 1)

Out of the given choices of equations (1, 2, 3 & 4) for line B choice 1 (y = –x + 3) and choice 3 (y = –2x + 7) shows negative slope.

Do you see that.......
Click to expand...
i'm working on BBB's then I will check yours. thanks, Doc.
 
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