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2 years ago

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Why do translations produce parallel lines

1 answer:

pav-90 [236]2 years ago

7 0

Answer:The distance between the lines stays constant, and they never intersect. In other words, you can translate (move) either line by that constant distance, in some direction, to get the other line. It's just like how when you change the y-intercept but keep the slope the same, you get parallel lines.

Step-by-step explanation:

Hope this helps ツ

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c(x) is a function, then we will solve the problem for two different functions.

1. If $c(x)=\frac{x}{0.5}+x$

Then

$y=c(x)$

$y=\frac{x}{0.5}+x$

Using each of the values for x we have.

When x=0 the result is: $y=\frac{0}{0.5}+0=0$

When x=0.008 the result is: $y=\frac{0.008}{0.5}+0.008=0.016+0.008=0.024$

When x=0.027 the result is: $y=\frac{0.027}{0.5}+0.027=0.054+0.027=0.081$

When x=0.064 the result is: $y=\frac{0.064}{0.5}+0.064=0.128+0.064=0.192$

When x=0.125 the result is: $y=\frac{0.125}{0.5}+0.125=0.25+0.125=0.375$

When x=0.216 the result is: $y=\frac{0.216}{0.5}+0.216=0.432+0.216=0.648$

When x=0.343 the result is: $y=\frac{0.343}{0.5}+0.343=0.686+0.343=1.029$

When x=0.512 the result is: $y=\frac{0.512}{0.5}+0.512=1.024+0.512=1.536$

When x=0.729 the result is: $y=\frac{0.729}{0.5}+0.729=1.458+0.729=2.187$

When x=1 the result is: $y=\frac{1}{0.5}+1=2+1=3$

2. If $c(x)=sin(x)+2x$

Then

$y=c(x)$

$y=sin(x)+2x$

Using each of the values for x we have.

When x=0 the result is: $y=sin(0)+2(0)=0$

When x=0.008 the result is: $y=sin(0.008)+2(0.008)=0.000139+0.016=0.016139$

When x=0.027 the result is: $y=sin(0.027)+2(0.027)=0.000471+0.054=0.054471$

When x=0.064 the result is: $y=sin(0.064)+2(0.064)=0.001117+0.128=0.129117$

When x=0.125 the result is: $y=sin(0.125)+2(0.125)=0.002182+0.25=0.252182$

When x=0.216 the result is: $y=sin(0.216)+2(0.216)=0.003769+0.432=0.435769$

When x=0.343 the result is: $y=sin(0.343)+2(0.343)=0.005986+0.686=0.691986$

When x=0.512 the result is: $y=sin(0.512)+2(0.512)=0.008936+1.024=1.032936$

When x=0.729 the result is: $y=sin(0.729)+2(0.729)=0.012723+1.458=1.470723$

When x=1 the result is: $y=sin(1)+2(1)=0.017452+2=2.017452$

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