# 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.

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#### Explanation

Explain in detail...

#### Explanation:

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Feb 22, 2018

$\left[- \frac{1}{2} , 3\right]$

#### 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 $m = 12$:
$y = 12 x + 6$
We want $x$ when $y = 0$, so
$0 = 12 x + 6$
$12 x = - 6$
$x = - \frac{1}{2}$

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

Therefore the range of x-ints is $- \frac{1}{2}$ to $3$, inclusive.

This is formalized in interval notation as:
$\left[- \frac{1}{2} , 3\right]$

PS:
Interval notation:
$\left[x , y\right]$ is all values from $x$ to $y$ inclusive
$\left(x , y\right)$ is all values from $x$ to $y$, exclusive.
$\left(x , y\right]$ is all values from $x$ to $y$ excluding $x$, including $y$
...
"[" means inclusive, "(" means exclusive.
Note: $\infty$ is always exclusive. so $x \ge 3$ is $\left[3 , \infty\right)$

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