Question

Consider the line y=-3x+3.

Find the equation of the line that is parallel to this line and passes through the point (-4, 5).
Find the equation of the line that is perpendicular to this line and passes through the point (-4, 5).

Equation of parallel line:
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3
Equation of perpendicular line:

Answer 1

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

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`