The line with equation $y = m x + 6$ $y=mx+6$ has a slope, m, such that $m \in [- 2, 12]$ $m ∈ [-2,12]$ . 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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The line with equation $y = m x + 6$ $y=mx+6$ has a slope, m, such that $m \in [- 2, 12]$ $m ∈ [-2,12]$ . 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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Answer 1 · 2018-02-22T01:02:17

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

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

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

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

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

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

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

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

The line with equation y=mx+6y=mx+6 has a slope, m, such that m∈[−2,12]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

Explanation:

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