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.
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
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
Hello, symmetry!
You may be expect to derive that formula . . .
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