The line with equation y=mx+6 has a slope, m, such that m ∈ [-2,12]. Use an interval to describe the possible x-intercepts of the line? Please explain in detail how to get the answer.

1 Answer
Feb 22, 2018

[-1/2, 3]

Explanation:

Consider the high and low values of the slope to determine the high and low value of the x-int. Then we can phrase the answer as an interval.

High:
Let m=12:
y=12x+6
We want x when y=0, so
0=12x+6
12x=-6
x=-1/2

Low:
Let m=-2
Likewise:
0=-2x+6
2x=6
x=3

Therefore the range of x-ints is -1/2 to 3, inclusive.

This is formalized in interval notation as:
[-1/2, 3]

PS:
Interval notation:
[x,y] is all values from x to y inclusive
(x,y) is all values from x to y, exclusive.
(x, y] is all values from x to y excluding x, including y
...
"[" means inclusive, "(" means exclusive.
Note: oo is always exclusive. so x>=3 is [3,oo)