Through: (1,-2), perp. yo y=1/5x+5

Answer 1

Through: (1,-2), perp. yo y=1/5x+5

The line is in the slope intercept form so.....

y=1/5x+5 ............this is the slope intercept form....y = mx + b....where m = slope

Through: (1,-2), perp. y=1/5x+5

You want to research and verify the following 2 principles related to perpendicular lines.

The slopes of two perpendicular lines are negative reciprocals.

The product of the slopes of two perpendicular lines is -1 since

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Through: (1,-2), perp. y=1/5x+5

We need the slope.....or the m portion of the equation so for the line....rewritten we have...

y=1/5x+5.....the slope is m = 1/5....Right?

Now using the given principles a line perpendicular to this one has a slope that is the negative reciprocal...hmmm

.....let's see....the reciprocal is 1/x....so the reciprocal in this case 5......but we are not done yet...

...the slope for a perpendicular line is "negative reciprocal".....so -5 is the slope of 2nd line....

....verify.....1/5 * -5 = -1.......that verifies the 2nd principle above.......

Through: (1,-2), perp. y=1/5x+5

....we also want the line to pass through a certain point....that is important because we can use the "point-slope" version of a line to find the equation of the 2nd line....like so.....

y−y1=m(x−x1).......y-(-2)=-5 (x - 1)......or y + 2= -5 (x-1)......or y + 2 = -5 x + 5

....subtract 2 from both sides......we have.....Y = -5 x + 5 - 2. or...y = -5 x + 3

..check the point (1,-2).....-2= -5 (1) + 3 =-2..it checks perfectly....

so the line y = -5 x + 3

....IS PERPENDICULAR TO THE LINE...

.....y=1/5x+5.....Correct?

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You can also GRAPH both of these lines to literally SEE the perpendicular lines cross each other......

Answer 2

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