Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.
2 answers:
Answer:
a. The equation of the parallel line to the given line is y = -4x + 19
b. The equation of the perpendicular line to the given line is y = x + 2
Step-by-step explanation:
Parallel lines have the same slopes
- If the slope of one of them is m, then the slope of the other is m
The product of the slopes of the perpendicular lines is -1
- If the slope of one of them is m, then the slope of the other is
- To find the slope of a perpendicular line to a given line reciprocal the slope of the given line and change its sign
The rule of the slope is m = , where
- (x1, y1) and (x2, y2) are the points on the line
The form of the equation of a line is y = m x + b, where
- m is the slope
- b is the y-intercept
Let us solve the question
∵ The given line passes through points (1, 6) and (2, 2)
∴ x1 = 1 and y1 = 6
∴ x2 = 2 and y2 = 2
→ Substitute them in the rule of the slope to find it
∵ m =
∴ The slope of the given line is -4
a.
∵ The line is parallel to the given line
∴ Their slopes are equal
∵ The slope of the given line = -4
∴ The slope of the parallel line = -4
→ Substitute its value in the form of the equation above
∴ y = -4x + b
→ To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ The parallel line passes through the point (4, 3)
∴ x = 4 and y = 3
∵ 3 = -4(4) + b
∴ 3 = -16 + b
→ Add 16 to both sides
∴ 3 + 16 = -16 + 16 + b
∴ 19 = b
→ Substitute it in the equation
∴ y = -4x + 19
The equation of the parallel line to the given line is y = -4x + 19
b.
∵ The line is perpendicular to the given line
∴ The product of their slopes is -1
→ Reciprocal the slope of the given line and change its sign
∵ The slope of the given line = -4
∴ The slope of the perpendicular line =
→ Substitute its value in the form of the equation above
∴ y = x + b
→ To find b substitute x and y in the equation by the coordinates
of any point on the line
∵ The perpendicular line passes through the point (4, 3)
∴ x = 4 and y = 3
∵ 3 = (4) + b
∴ 3 = 1 + b
→ Subtract 1 from both sides
∴ 3 - 1 = 1 - 1 + b
∴ 2 = b
→ Substitute it in the equation
∴ y = x + 2
The equation of the perpendicular line to the given line is y = x + 2
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Probability helps us to know the chances of an event occurring. The probability that the next customer will pay with cash as a percent to the nearest whole number is 64%.
<h3>What is Probability?</h3>Probability helps us to know the chances of an event occurring. The sum of all the probabilities of an event is always equal to 1. The formula for probability is given as,
Given that in the last week 71 customers paid cash, 4 customers used a debit card, and 36 customers used a credit card. Therefore, the total number of customers who came to the business last month is,
Total number of customers = 71 + 4 + 36 = 111
Now, the probability that the next customer will pay with cash is,
Probability
= Number of customers who pay with cash / Total number of customers
= 71 / 111
= 0.63963
To convert probability into percentage multiply it by 100%, therefore, the probability can be written as,
Probability = 0.63963 × 100%
= 63.963% ≈ 64%
Hence, the probability that the next customer will pay with cash as a percent to the nearest whole number is 64%.
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