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Andru [333]
3 years ago
9

What is the equation of the line that passes through (4, -1) and (-2,3)?

Mathematics
2 answers:
guajiro [1.7K]3 years ago
8 0

Answer:

y = -(2/3)x + 5/3

Step-by-step explanation:

Label the points that are given.  

(4, -1) = (x1, y1)

(-2, 3) = (x2, y2)

Step 1: Find the slope, denoted m

This is done by using the formula m = (y2 - y1)/(x2 - x1)

The slope for this problem is

m = (3 - (-1))/(-2 - 4)  

m = 4/-6 = -2/3

Step 2: The general form for a linear equation in slope-intercept form is  

y = mx + b where m is the slope and b is the y-intercept

Use what we know about our line to solve the rest. By using one of the given points, we have 3 of the 4 variables in the above equation. Pick either point, it doesn't matter which one. We'll use (4, -1), which is (x, y), and we know that  

m = -2 /3

The equation becomes...

-1 = -(2/3)(4) + b (now solve for b)

-1 =  -8/3 + b

-1 + 8/3 = b

-3/3 + 8/3 = b

5/3 = b

Plug that value into the general form...

y = -(2/3)x + 5/3

stich3 [128]3 years ago
4 0

Answer:

2x + 3y =  5.

Step-by-step explanation:

First find the slope  of the line:

Slope = (3 - (-1)) / (-2-4)

= 4/-6 = -2/3

Now we use the point slope form of a straight line:

y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.

y - 3 = -2/3(x - (-2))

y - 3 = -2/3(x + 2)

3y - 9 = -2x - 4

2x + 3y = 5.

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The length of time to complete a door assembly on an automobile factory assembly line is normally distributed with a mean of 6.7
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We need to work out the z-value of each question to work out the probability

Question a)

We have
X = 5 minutes
The mean, μ = 6.7 minutes
Standard deviation, σ = 2.2 minutes
z-score = (X - μ) / σ = (5 - 6.7) / 2.2 = -0.77

We want to find the probability of z < -0.77 so we read the z-table for the value of z on the left of -0.77 we have the probability P(z< -0.77) = 0.2206

The table is attached in picture 1 below

The probability of assembly time less than 5 minutes is 0.2206 = 22.06%

Question b)

z-score = (10-5) / 2.2 = 2.27

Reading the z-table for P(z<2.27) = 0.9884
The table reading is shown in the second picture below

The probability the assembly time will be less than 10 minutes is 0.9884

We can use this information to find the probability of the assembly time will be more than 10 minutes  = 1 - 0.9884 = 0.0116 = 1.16%

Question c)

The value of z between 5 minutes and 10 minutes is

P(-0.77<z<2.27) = P(z<2.27) - P(z< -0.77)
P(-0.77<z<2.27) = 0.9884 - 0.2206 = 0.7678 = 76.78%


6 0
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