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OverLord2011 [107]
3 years ago
8

The line with equation y= 2x + 3 is reflected in the x-axis.

Mathematics
1 answer:
nadya68 [22]3 years ago
3 0

Step-by-step explanation:

When a graph is reflected about the x-axis, their x-intercept(s) are invariant point(s).

For y = 2x + 3, the x-intercept is -3/2.

Also the slope of the line graph when reflected about the x-axis will change from m to -m.

Therefore the new slope is -2.

We have y = -2x + c.

When x = -3/2, y = 0.

=> (0) = -2(-3/2) + c, c = -3.

Hence the answer is y = -2x - 3. (E)

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so, we have two points, let's check with that,

</span>\bf \begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&&(~ -10 &,& 12~) &#10;%  (c,d)&#10;&&(~ 16 &,& -1~)&#10;\end{array}&#10;\\\\\\&#10;% slope  = m&#10;slope =  m\implies &#10;\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-12}{16-(-10)}\implies \cfrac{-1-12}{16+10}&#10;\\\\\\&#10;\cfrac{-13}{26}\implies -\cfrac{1}{2}
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</span>\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)} y-12=-\cfrac{1}{2}[x-(-10)]&#10;\\\\\\&#10;y-12=-\cfrac{1}{2}(x+10)\implies y-12=-\cfrac{1}{2}x-5\implies y=-\cfrac{1}{2}x+7<span>
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