Write and equation in standard form for a line that is (a) parallel (b) perpendicular to the line with an equation of y= 3x - 5
that passes through the point (5,8)
1 answer:
Answer:
(a) 3x -y = 7
(b) x +3y = 29
Step-by-step explanation:
(a) The standard form of the given line is ...
3x -y = 5
The parallel line will have a constant on the right that makes it go through (5, 8), so it will be ...
3x -y = 3(5) -(8)
3x -y = 7
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(b) The perpendicular line will have coefficients for x and y swapped and one of them negated. Again, the constant is chosen to make it go through (5, 8).
x + 3y = (5) +3(8)
x + 3y = 29
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Answer:
A. f(x): , g(x): (0,0)
B. f(x): 'y= 0' as horizontal asymptote, g(x): 'x= 4' as vertical asymptote.
Step-by-step explanation:
We are given the functions, and graph of g(x).
Part A: We know that,
<em>'Y-intercepts are the points where the graph of the function crosses y-axis'.</em>
<em>That is, 'y-intercept is obtained when x= 0'.</em>
So, we have,
When x= 0, i.e.
.
Thus, the y-intercept of function f(x) is the point .
Also, from the graph of g(x), we see that, the graph crosses y-axis at the point (0,0).
Thus, the y-intercept of g(x) is (0,0).
Part B: We know that,
<em>'Asymptotes are the line or curves approaching the graphs of the functions arbitrarily close'.</em>
Now, as we have the function f(x) is a rational function and the degree of numerator is less than the degree of the denominator.
So, the function f(x) will have 'y= 0' as the horizontal asymptote.
Also, from the graph of the function g(x), we see that,
The line 'x= 4' is the vertical asymptote as it is approaching the graph closely.
So, the function g(x) have 'x= 4' as the vertical asymptote.