ANSWER
Vertical asymptote:
x=1
Horizontal asymptote:
y=1
EXPLANATION
The given rational function is
The vertical asymptote occurs at
The vertical asymptotes is x=1
The degree of the numerator is the same as the degree of the denominator.
The horizontal asymptote of such rational function is found by expressing the coefficient of the leading term in the numerator over that of the denominator.
y=1
4x - 3y = 15
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Explanation:
The two points (-1,-1) and (2,3) are marked on the line
Let's find the slope of the line through those two points.
The slope is 4/3 meaning we go up 4 and to the right 3.
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Parallel lines have equal slopes, but different y intercepts. We'll need to see which of the four answer choices have a slope of 4/3.
Solve the equation in choice A for y. The goal is to get it into y = mx+b form so we can determine the slope m.
Equation A has a slope of -3/4 and not 4/3 like we want.
Therefore, this answer choice is crossed off the list.
Follow similar steps for choices B through D. I'll show the slopes of each so you can check your work.
We have a match with equation D. Therefore, the equation 4x-3y = 15 is parallel to the given line shown in the graph.
You can use graphing tools like Desmos or GeoGebra to confirm the answer.