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# Help?

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1. A line with slope 2/3 contains the point P(-18, -12). What is the x-intercept of the line?

2. The graphs of y=|x| and y=-x^2-3x-2 are drawn. For every x, a vertical segment connecting these two graphs can be drawn as well. Find the smallest possible length of one of these vertical segments.

Mar 18, 2020
edited by qwertyzz  Mar 18, 2020

#1
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1.  The  equation of the line can be  found  as follows :

y = (2/3) ( x + 18)  - 12

To find  the  x intercept, let  y  =  0  ......so we have....

0  = (2/3)(x + 18)  - 12         add  12 to both sides

12  = (2/3) ( x + 18)      multiply both sides  by (3/2)

18  = x + 18         subtract  18 from both sides

0  = x    ⇒  the   x intercept

Mar 18, 2020
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2. The graphs of y=|x| and y=-x^2-3x-2 are drawn. For every x, a vertical segment connecting these two graphs can be drawn as well. Find the smallest possible length of one of these vertical segments.

Look at  the graph here : https://www.desmos.com/calculator/p7iq0yf8z5

Note  that  the  vertex  of  the parabola  occurs at  (-1.5, .25)

When a  vetical ine is drawn at x  =  -1.5, the line will intersect the absolute value graph at (-1.5, 1.5)

So......the distance between  these two points is

1.5 -  .25   =

1.25  units

Mar 18, 2020
edited by CPhill  Mar 18, 2020
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Thank you!

qwertyzz  Mar 19, 2020