# 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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### 4 Answers

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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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.

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.

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