functions of a line HELP?

Question

Derive the value of k for which the line 4x+ky = 5 is parallel to the y-axis.

Also, Derive the value of k for which the line 4x+ky = 5 has equal x and y intercepts.

2. Show that if the x-intercept of a line is a and the y-intercept is b, then the equation of this line can be written in the form x/a+y/b=1.

Answer 1

For the first one, if the line is parallel to the y axis, it is a vertical line - the equation has to say something like x = 3 or x = -2. There would be no y component for that equation. So for your equation, k = 0 so that the y component goes away, and you're left with 4x = 5, or x = 5/4.

The second one is interesting - intercepts happen when x = 0 or y = 0 - the line crosses the y- and x-axis. So for this, we need a few equations to get started:

Finding the y-intercept - set x = 0:
4x + ky = 5
ky = 5

Finding the x-intercept - set y = 0:
4x + ky = 5
4x = 5
x = 5/4

So we need y = 5/4 as well:
ky = 5
k(5/4) = 5
k = 4

So this says that if k = 4, then your line will have intercepts at (0, 5/4) and (5/4, 0).