Answer:
-5/3
Step-by-step explanation:
Parallel lines are lines which have the exact same slope but different y-intercepts. We can find the slope by converting to slope-intercept form, y=mx+b from standard form.
We convert by using inverse operations to isolate y.
5x+3y=7
5x-5x+3y=7-5x
0x+3y=-5x+7
3y=-5x+7
.
The slope is -5/3. SInce parallel lines have the same slope, the slope for a parallel line will be -5/3.
Solution
Asymptote:
Vertical Asymptote
- The vertical asymptotes of a rational function are determined by the denominator expression.
- The expression given is:
- The denominator of (x- 36) determines the asymptote line.
- The vertical asymptote defines where the rational function isundefined. Iin order for a rational function to be undefined, its denominator must be zero.
- Thus, we can say:
- Thus, the vertical asymptote is
Horizontal Asymptote:
- The horizontal asymptote exists in two cases:
1. When the highest degree of the numerator is less han the degree of the demnominator. In this case, the horizontal asymptote is y = 0
2. When the highest degee sof the numerator and tdenominator are the same. In this case, the horizontal asymptote is
- For our question, we can see that the highest degrees of the numerator and denominator are the same. Thus, we have the Horizontal Asymptote to be:
End behavior:
- The end behavior is examining the y-values of the function as x tendsto negative and positive infinity.
- Thus, we have that:
Final Answers
Asymptotes:
End behavior:
