Show that an equation for a line with nonzero x-and y-intercepts can be written as (x/a) + (y/b) = 1 where a is the x-intercept and

b is the y-intercept. This is called the INTERCEPT FORM of the equation of a line.

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- Jan 16th 2007, 02:51 PMsymmetryEquation of the Line
Show that an equation for a line with nonzero x-and y-intercepts can be written as (x/a) + (y/b) = 1 where a is the x-intercept and

b is the y-intercept. This is called the INTERCEPT FORM of the equation of a line. - Jan 16th 2007, 03:15 PMtopsquark
The x-intercept will be of the form (a, 0). Does this fit the equation?

Check!

The y-intercept will be of the form (0, b). Does this fit the equation?

Check!

If you have a need to show that this equation is indeed a line, then you can solve it for y:

which is the slope-intercept form for a line.

-Dan - Jan 16th 2007, 06:18 PMsymmetryok
So, I simply needed to set y = 0 to find the x-intercepts and set x = 0 to find the y-intercepts.

How about that?

Thanks! - Jan 16th 2007, 06:45 PMtopsquark
Yup! What a lot of students tend to forget is that the y - intercept, for example, is a

__point__. So when we say the y - intercept is "b" we are using a short-hand and being a bit sloppy: we really should be saying the y - intercept is the point (0, b). The same goes for the x - intercept.

-Dan - Jan 16th 2007, 07:49 PMSoroban
Hello, symmetry!

You may be expect to*derive*that formula . . .

Quote:

Show that an equation for a line with nonzero x-and y-intercepts

can be written as: .

where is the x-intercept and is the y-intercept.

We are given two points on the line: . and .

The slope of the line is: .

The line through with slope is:

. . . .

Divide through by