Question

Answer the following questions:

a) Can every line be written in slope-intercept form?
b) Does every line have two distinct intercepts?
c) Are there lines that have no intercepts?

Answer 1

(a) No, every equation of line can't be written in slope Intercept form which can be explained in the following way.

→y=m x +c, where m is slope of line and c is y intercept.

Suppose a line is , ax +by+c=0

by=-ax -c

`y=(-ax)/(b)-(c)/(b)`

if, c=0, then line will be not in slope intercept form.

(b) NO,

Every line has two intercepts , one is called X intercept and another one is Y intercept.

Equation of line in Intercept form

ax +by+c=0

by+ax =-c

`(x)/((-c)/(a))+(y)/((-c)/(b))=1`

But if,c=0,equation of line can't be written in intercept form.

(c)

Yes, all lines which passes through Origin have no intercepts that is X intercept and Y intercept.

Equation of these lines are

y= mx, where m is slope of the line.

Answer 2

A. The slope intercept form of a line is generally expressed as, y = mx + b. Not all the lines may be expressed this way because some lines do not have y-intercept.
B. Not all lines have two distinct intercepts because vertical and horizontal lines only has one intercepts each.
C. No. Each line will have 1 or more intercepts.