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# At which point do the following lines intersect?

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Intern
Joined: 26 Apr 2018
Posts: 39
At which point do the following lines intersect?  [#permalink]

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29 Sep 2018, 06:52
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Difficulty:

15% (low)

Question Stats:

78% (01:13) correct 22% (02:05) wrong based on 36 sessions

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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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Director
Joined: 19 Oct 2013
Posts: 509
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: At which point do the following lines intersect?  [#permalink]

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29 Sep 2018, 08:36
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

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Senior SC Moderator
Joined: 22 May 2016
Posts: 2197
At which point do the following lines intersect?  [#permalink]

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29 Sep 2018, 08:38
1
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)

*$$y = f(x) = mx + b$$
$$y=mx+b$$
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 $$x$$
Manager
Joined: 01 Jan 2018
Posts: 69
Re: At which point do the following lines intersect?  [#permalink]

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29 Sep 2018, 08:57
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? &nbs [#permalink] 29 Sep 2018, 08:57
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