Find the equation of the line containing the point (-1, 5) and having a slope: -2
1 answer:
Step-by-step explanation:
<u>Slope-intercept form:</u>
<u />
m = slope
b = y-intercept
The slope is given; -2.
We have to figure out what the y-intercept is.
The y-intercept is where the line crosses the y-axis, or when x = 0.
Given the point, (-1, 5), we can determine what the y-intercept is with the slope.
The slope is describing that per every x, y decreases by 2.
-1 + 1 = 0 (x)
5 - 2 = 3 (y)
3 is the y-intercept
<u>Substitute the slope and the y-intercept in the slope-intercept form equation:</u>
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Answer:
A. lim [x ⇒ -∞] g(x) = -5 . . . . . . written in text form, not typeset
Step-by-step explanation:
A horizontal asymptote is a line that the function approaches but never reaches. It represents the limiting value that the function can have. (The function can come as close to that value as you like for some value of x, but can never actually reach that value.)
Here, you're told the asymptote for negative x values is -5. That means g(x) gets closer and closer to -5 for values of x that are more and more negative. That is, as x approaches infinity, g(x) approaches -5. We say -5 is the limit of g(x) as x approaches negative infinity.
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The attached graph shows a function that has characteristics like those of g(x).
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This question is about vocabulary: what is the meaning of "asymptote" and "limit", and how do you read a description of a limit written using math language.
