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In the equation mx + 5 = y, m is a constant. If x = 2 when y = 1, when

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Bunuel
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In the equation mx + 5 = y, m is a constant. If x = 2 when y = 1, when [#permalink] New post   24 Mar 2022, 04:15
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In the equation mx + 5 = y, m is a constant. If x = 2 when y = 1, when is the value of x when y = –1?

A. −1
B. 0
C. 1
D. 2
E. 3
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IanStewart
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Re: In the equation mx + 5 = y, m is a constant. If x = 2 when y = 1, when [#permalink] New post   24 Mar 2022, 04:38
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y = mx + 5 is a line with slope m, and y-intercept 5, so the point (0, 5) is on the line. We're also told (2, 1) is on the line, so the line is falling as you move to the right. The point where y = -1 must therefore be to the right of the point (2, 1), and its x-coordinate must therefore be greater than 2, and the only plausible answer is 3, answer E. Or you could do a bit more work to learn m = -2 and substitute.
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Re: In the equation mx + 5 = y, m is a constant. If x = 2 when y = 1, when [#permalink] New post   27 Sep 2023, 08:29
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Bunuel wrote:
In the equation \(mx + 5 = y\), m is a constant. If \(x = 2\) when \(y = 1\), when is the value of \(x\) when \(y = –1\)?

A. −1
B. 0
C. 1
D. 2
E. 3

We have \(mx + 5 = y\)

Or, \(m*2 + 5 = 1\)

Or, \(2m = -4\)

So, \(m = -2\)

Now to find the value of \(x\) when \(y = -1\) will be -

\(-2x + 5 = -1\)

Or, \(-2x = -6\)

Or, \(x = 3\), Answer will be (E)
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Re: In the equation mx + 5 = y, m is a constant. If x = 2 when y = 1, when [#permalink] New post   27 Sep 2023, 01:26
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Bunuel wrote:
In the equation mx + 5 = y, m is a constant. If x = 2 when y = 1, when is the value of x when y = –1?
A. −1
B. 0
C. 1
D. 2
E. 3


Solution:

  • Given \(y=mx+5\)

  • \(x=2\) and \(y=1\)
      \(⇒1=2m+5\)
    or \(m=-2\)

  • So, when \(y=-1\)
      \(⇒-1=-2x+5\)
      \(⇒x=3\)

Hence the right answer is Option E
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Re: In the equation mx + 5 = y, m is a constant. If x = 2 when y = 1, when [#permalink] New post   27 Sep 2023, 08:38
mx+5=y, and when
x=2, y=1. We can substitute these values into the equation:
m(2)+5=1
Now, solve for m:
2m+5=1
m=−2
Now, we want to find the value of
x when
y=−1. We can use the value of
m we found to do this:
mx+5=y
−2x+5=−1
−2x=−6
Finally, divide by -2 to solve for x:
x=(−6)/(−2)
x=3
So, when
y=−1, the value of x is 3.
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Re: In the equation mx + 5 = y, m is a constant. If x = 2 when y = 1, when [#permalink]
27 Sep 2023, 08:38
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