Chris will work as a landscaper over the summer. He buys $240 worth of supplies and will spend $10 each week on advertising. If
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Answer:
a) The slope of the line is parallel to the another line m=4
b) The slope of the line is perpendicular to the another line m=
Step-by-step explanation:
Step1:-
<u>Slope of a line</u><u> :-</u>
If θ is the inclination of a line 'l' then tanθ is called the slope or gradient of the line 'l'.The slope of a line is denoted by m=tanθ
The slope of a line given two points m=
<u>Parallel lines:-</u>
<u>Two </u>non-vertical lines are parallel if and only if their slopes are parallel
<u>Perpendicular lines:-</u>
<u>Two </u>non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.
<u>Step 2</u>:-
a)The slope of a line when given two points (-1,-4) and (0,0)
<u>Two </u>non-vertical lines are parallel if and only if their slopes are parallel
Therefore the slope of the line that is parallel to the another line
<u>Step 3</u>:-
b) <u>Two </u>non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.
Therefore the slope of the line is perpendicular to the another line is
Answer:
The discontinuity is x = 4
There no holes
The equation of the vertical asymptote is x = 4
The x intercept is 2
The equation of the horizontal asymptote is y = 1
Step-by-step explanation:
* Lets explain the problem
∵
- To find the point of discontinuity put the denominator = 0 and find
the value of x
∵ The denominator is x - 4
∵ x - 4 = 0 ⇒ add 4 to both sides
∴ x = 4
* The discontinuity is x = 4
- A hole occurs when a number is both a zero of the numerator
and denominator
∵ The numerator is x - 2
∵ x - 2 = 0 ⇒ add 2 to both sides
∴ x = 2
∵ The denominator is x - 4
∵ x - 4 = 0 ⇒ add 4 to both sides
∴ x = 4
∵ There is no common number makes the numerator and denominator
equal to 0
∴ There no holes
- Vertical asymptotes are vertical lines which correspond to the zeroes
of the denominator of the function
∵ The zero of the denominator is x = 4
∴ The equation of the vertical asymptote is x = 4
- x- intercept is the values of x which make f(x) = 0, means the
intersection points between the graph and the x-axis
∵ f(x) = 0
∴ ⇒ by using cross multiplication
∴ x - 2 = 0 ⇒ add 2 to both sides
∴ x = 2
* The x intercept is 2
- If the highest power of the numerator = the highest power of the
denominator, then the equation of the horizontal asymptote is
y = The leading coeff. of numerator/leading coeff. of denominator
∵ The numerator is x - 2
∵ The denominator is x - 4
∵ The leading coefficient of the numerator is 1
∵ The leading coefficient of the denominator is 1
∴ y = 1/1 = 1
* The equation of the horizontal asymptote is y = 1
