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At which point do the following lines intersect?

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At which point do the following lines intersect?  [#permalink]

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New post 29 Sep 2018, 07:52
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At which point do the following lines intersect?

f(x)=−4x+3

g(x)=5x+39



a) (-4,39)

b) (-4,19)

c) (0,0)

d) (4,-39)

e) (4,19)



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Re: At which point do the following lines intersect?  [#permalink]

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New post 29 Sep 2018, 09:36
To find the points at which they intersect

We equate both sides

-4x + 3 = 5x + 39
9x = -36
x = -4

Now substitute back in the function

-4 * -4 + 3 = 16 + 3 = 19

So (-4,19) answer choice B

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At which point do the following lines intersect?  [#permalink]

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New post 29 Sep 2018, 09:38
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bettatantalo wrote:
At which point do the following lines intersect?

f(x)=−4x+3

g(x)=5x+39



a) (-4,39)

b) (-4,19)

c) (0,0)

d) (4,-39)

e) (4,19)

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\(f(x)=y\) and \(g(x)=y\)

Just rewrite f(x) and g(x) as \(y\). Doing so yields two linear equations in slope-intercept form*: \(y=mx+b\)

So \(f(x)=−4x+3\) becomes
\(y=-4x+3\)
AND
\(g(x)=5x+39\) becomes
\(y=5x+39\)

At the point of intersection, lines, expressed by their equations, have the same (x,y) coordinates.

We use \(y=y\) from equations above to find the x-coordinate.

Set the linear equations equal:

\(-4x +3 = 5x+39\)
\(-9x=36\)
\(x =\frac{36}{-9}=-4\)

The lines intersect at x-coordinate (-4). Plug that (-4) back into either equation to find the y-coordinate

\(y= -4x +3\)
\(y =(-4)(-4)+3\)
\(y=(16+3)=19\)

The point of intersection (x,y) is (-4,19)

Answer B

*\(y = f(x) = mx + b\)
\(y=mx+b\)
is slope-intercept form
See HERE for a good explanation of slope intercept form.

Linear functions have one dependent variable, y, and one independent variable, x. Similarly, the slope-intercept form of an equation also has dependent variable \(y\) and independent variable \(x\)

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Re: At which point do the following lines intersect?  [#permalink]

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New post 29 Sep 2018, 09:57
The point where the lines intersect will satisfy both the equations.
So, 4x+3=5x+39=>x=-4
Substituting in any one equation we get y= 19
So, B is the correct choice.
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Re: At which point do the following lines intersect?   [#permalink] 29 Sep 2018, 09:57
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