Write an equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4)
1 answer:
Answer:
The equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4) will be:
- y = 3x-13
Step-by-step explanation:
Given the equation
y + 5 = 3(x - 1)
Writing in the slope-intercept form
y=mx+b
where m is the slope and b is the y-intercept
y = 3(x-1) -5
y = 3x-3-5
y = 3x - 8
Thus, the slope = m = 3
We know that the parallel lines have equal slopes.
So, the slope of a parallel line is also 3
Using the point-slope form of the line equation
substituting the values m = 3 and the point (3, -4)
y-(-4)=3(x-3)
y+4 = 3x-9
y = 3x-9-4
y = 3x-13
Thus, the equation for a line that is parallel to y + 5 = 3(x - 1) and goes through the point (3,-4) will be:
- y = 3x-13
You might be interested in
Answer:
11.51% probability that the sample average will be less than 182
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the sample average will be less than 182
This is the pvalue of Z when X = 182. So
By the Central Limit Theorem
has a pvalue of 0.1151
11.51% probability that the sample average will be less than 182