the equation of a line with the same x-intercept as the line x-2y=5 and the same y-intercept as the line 5x-2y=8

Question

the equation of a line with the same x-intercept as the line x-2y=5 and the same y-intercept as the line 5x-2y=8

Answer 1

Remember the definitions:

   y-intercept = place where line crosses y-axis; x=0 here

   x-intercept = place where line crosses x-axis; y=0 here

 

The line x-2y=5 is just x-0=5 or x=5 when y=0.  The x=intercept is (5,0).

 

The line 5x-2y=8 is just -2y=8 or y=-4 when x=0.  The y=intercept is (0,-4).

 

IMPORTANT:  The line that "has the same x-intercept as .. and the same y-intercept as ..." contains those two points.  So, using them to find the equation of that line:

 

  (y - y₁) = ( (y₂ - y₁) / (x₂ - x₁) )(x -x₁)     [note: slope-intercept form]

   y - 0 = ((-4-0)/(0-5))(x-5)

    y = (4/5)x - 4

 

To check that both intercepts are on that line, plug in the (x,y) values; they satisfy the equation.

 

Now, since the original equations were given in Standard Form, you may want to represent the answer that way:

    4x -5y = 20

 

Answer 2

I'll bet you can do this--just go one step at a time.

 

First line: x - 2y = 5.  Find its x-intercept (by setting y to zero).  Call that a

 

second line: 5x - 2y = 8. Find its y-intercept (by setting x to zero(.  Call that b

 

There is a wonderful form of the equation of a line called INTERCEPT FORM:

 

x/a + y/b = 1.

 

Otherwise, you can use y = mx + b and you already know b, the y-intercept, and you can substitute (a,0) into this and you'll find m, and the problem will be solved in that way (probably more familiar to your teacher).