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vladimir2022 [97]
2 years ago
15

Consider the line y=-3x+3.

Mathematics
1 answer:
emmainna [20.7K]2 years ago
7 0

Answer:

y= 3x+17; y= -\frac13x +\frac{11}3

Step-by-step explanation:

First problem. If you want a parallel to a given line, you keep the slope.

Then we use the point-slope form of a line

y-y_0=m(x-x_0) and we plug in there everything we need.

y-5=3(x+4) \rightarrow y=3x+12+5\\y=3x+17

The second is quite similar. This time we want the perpendicular. It means that the product of the slopes has to be -1.

3\cdot m = -1 \rightarrow m=-\frac13

At this point we have everything, let's replace and write down the line in a better looking form

y-5=-\frac13(x+4) \rightarrow y= -\frac13 x -\frac43 +5\\y= -\frac13x -\frac43 +\frac{15}3 \rightarrow y= -\frac13x +\frac{11}3

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