What is the equation of a line that passes through the point (6, 0) and the distance between this point and where it touches the y axis is 10.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The line passes through the point (6, 0). This is the x-intercept. The y- intercept is (0, y1). As the distance between (6, 0) and the point (6, 0) is 10:

6^2 + y^2 = 10^2

=> y^2 = 100 - 36 = 64

y = 8 and y = -8

There are two two lines that satisfy the given condition with y-intercepts y = 8 and y = -8.

The equation of the two lines is: x/6 + y/8 = 1 and x/6 - y/8 = 1

=> 8x + 6y = 48 and 8x - 6y = 48

The required equation of the line is 8x + 6y = 48 and 8x - 6y = 48

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vindiesel | Student, Undergraduate | eNotes Newbie

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mcdowell-mountain-ranch-homes

 

The intersect on the y axis is as explained above as 2 lines meet the conditions of the distance between the 2 points. The 8 is arrived at by solving the missing side of the right triangle using the Pithagore trick.

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bernardg2000 | eNotes Newbie

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Another way to approach it is to consider that you can build the equation by positionning a point on the extension of the line and call it  point P with coordinates (x,y).

You know the slope (8/6) from the previous solution

Therefore (y-0)/(x-6)=8/6

y/(x-6)=8/6

6y=8x-48 or 8x-6y=48

Solve now for the negative slope.

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bernardg2000 | eNotes Newbie

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First draft the line on paper. Visualizing helps a lot.

The intersect on the y axis is as explained above as 2 lines meet the conditions of the distance between the 2 points. The 8 is arrived at by solving the missing side of the right triangle using the Pithagore trick.

Let us focus on the line which has a positive slope which is:

m=(y2-y1)/(x2-x1) ; the 2 points being where the line intercepts the x and y axis.

m=0-(-8)/(6-0)=8/6

The equation of a straight line is of the form:

y=mx+b where m is the slope and b is the y intercept

y=(8/6)x - 8

This develops to 8x-6y=48

Work out the other line the same way and it will lead to 

8x+6y=48

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