Question 65275
<pre>find the equation of the line that passes through the intersection 
of the given pair of lines and satisfies the other given condition. 
graph. 

3x + 4y - 2 = 0, 3x - 4y + 1 = 0; the intercepts are equal.
<font size = 5><b>
First we must find the point of intersection by 
the system of two equations in two unknowns
 
3x + 4y - 2 = 0 
3x - 4y + 1 = 0

You can solve that system of equations and get
 x = 1/6, y = 3/8

Now the problem become:

Find the equation of the line through the point
(1/6, 3/8)
which has equal intercepts.  To have equal 
intercept, if the point ehere the line crosses 
the y-axis is (0, b), then the point where the 
line crosses the x-axis is (b, 0).

So we find its slope by the slope formula

(x<sub>1</sub>, y<sub>1</sub>) = (0, b) and (x<sub>2</sub>, y<sub>2</sub>) = (b, 0)

     y<sub>2</sub> - y<sub>1</sub>     (0) - (b)     -b
m = --------- = ----------- = ---- = -1 
     x<sub>2</sub> - x<sub>1</sub>     (b) - (0)      b

Now we use the point slope form with m = -1 
and (x<sub>1</sub>, y<sub>1</sub>) = (1/6, 3/8)

y - y<sub>1</sub> = m(x - x<sub>1</sub>) 
 
y - (3/8) = -1(x - 1/6)

y - 3/8 = -x + 1/6

Now we multiply through by LCD = 24 to clear 
of fractions: 

24y - 9 = -24x + 4

24y + 24x - 13 = 0

or solve for y and get

y = -x + 13/24 

The two equal intercepts are at points 

(13/24, 0) and (0, 13/24)

Edwin</pre>