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In the xy-coordinate plane, lines j and k intersect at point
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04 Oct 2018, 16:38
04 Oct 2018, 16:38
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In the xy-coordinate plane, lines j and k intersect at point (1, 3). If the equation of line j is y = ax + 10, and the equation of k is y = bx + a, where a and b are constants, what is the value of b?
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10
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Re: In the xy-coordinate plane, lines j and k intersect at point
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05 Oct 2018, 07:30
05 Oct 2018, 07:30
3
sandy wrote:
In the xy-coordinate plane, lines j and k intersect at point (1, 3). If the equation of line j is y = ax + 10, and the equation of k is y = bx + a, where a and b are constants, what is the value of b?
Show: :: OA
10
We're told that the point (1, 3) lies on line j
So, it must be the case that x = 1 and y = 3 is a solution to the equation for line j: y = ax + 10
Plug in those x- and y-values to get: 3 = a(1) + 10
So, we have: 3 = a + 10, which means a = -7
We're also told that the point (1, 3) lies on line k
So, it must be the case that x = 1 and y = 3 is a solution to the equation for line k: y = bx + a
Plug in those x- and y-values to get: 3 = b(1) + a
Since we now know that a = -7, we can write: 3 = b(1) + (-7)
We get: 3 = b - 7
Solve: b = 10
Answer: 10
Cheers,
Brent
Re: In the xy-coordinate plane, lines j and k intersect at point
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10 May 2020, 12:20
10 May 2020, 12:20
sandy wrote:
In the xy-coordinate plane, lines j and k intersect at point (1, 3). If the equation of line j is y = ax + 10, and the equation of k is y = bx + a, where a and b are constants, what is the value of b?
Show: :: OA
10
If (1,3) is the point of intersection of the two lines then when x=1 the equations are equal.
Hence..
ax + 10 = bx + a
Substitute x=1
a + 10 = b + a
Reduce a from both sides.
10=b
Therefore, b=10.
