SOLUTION: 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 intercept

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.

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

(x1, y1) = (0, b) and (x2, y2) = (b, 0)

     y2 - y1     (0) - (b)     -b
m = --------- = ----------- = ---- = -1 
     x2 - x1     (b) - (0)      b

Now we use the point slope form with m = -1 
and (x1, y1) = (1/6, 3/8)

y - y1 = m(x - x1) 
 
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