What would be a line perpendicular to (2,3) (5,5)?
1 answer:
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Answer:
3x + 2y = 0 or y = -3/2x
Step-by-step explanation:
The relationship between a line and its perpendicular is that their slopes are opposite reciprocals of each other. So, the thing you need to know about the line through the two given points is its slope. That is found using the slope formula:
m = (y2 -y1)/(x2 -x1) . . . . . . where the two give points are (x1, y1) and (x2, y2)
Putting your point coordinates in this formula gives ...
m = (5 -3)/(5 -2) = 2/3
Then the perpendicular line will have a slope that is the opposite reciprocal:
slope of perpendicular = -1/m = -1/(2/3) = -3/2
You have not said whether the perpendicular line must meet any other requirement, so the simplest one we can write is ...
y = mx + b . . . . . m is the slope and b is the y-intercept
y = -3/2x . . . . . . has a y-intercept of 0 (goes through the origin)
Multiplying by 2 and adding 3x gives ...
3x + 2y = 0 . . . . . standard form equation
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<em>Comment on the attachment</em>
The geometry program I used to create the attachment wrote the equation of the line through the given points as ...
2x -3y = -5 . . . . . standard form equation
The equation of a perpendicular line can be created from this form by swapping the x- and y-coefficients and negating one of them. Simply swapping the coefficients would give ...
-3x +2y = <something>
In standard form, we want the leading coefficient to be positive, so we can choose to negate the x-coefficient. The <something> can be zero to make the line go through the origin.
3x +2y = 0 . . . . . a perpendicular in standard form
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If you need to have the line go through a particular point, you can determine the constant value (on the right of the = sign) by putting the point coordinates in for x and y.
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Method summary:
- find the slope of the given line
- determine its opposite reciprocal to find the slope of the perpendicular line
- use that new slope in an appropriate form to have the line go where you want it to go. (Point-Slope Form is often useful)
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Answer:
As the <em>p</em>-value is too small the null hypothesis will be rejected concluding that there is a higher proportion of people supporting the home team.
Step-by-step explanation:
The hypothesis to determine which team spectators at a football game support is:
<em>H₀</em>: There are equal proportions of people supporting the home team and the visiting team, i.e. <em>p</em>₁ = <em>p</em>₂.
<em>Hₐ</em>: There is a higher proportion of people supporting the home team than the visiting team, i.e. <em>p</em>₁ > <em>p</em>₂.
A <em>z</em>-test for difference between proportions can be used to perform the test.
The test statistic is:
Th decision rule is:
If the <em>p</em>-value of the test is less than the significance level <em>α </em>then the null hypothesis will be rejected and vice-versa.
The commonly used significance levels are 0.01, 0.05 and 0.10.
The <em>p</em>-value of the test is computed as, <em>p</em> = 0.002.
The <em>p</em>-value of the test is less than all the significance level.
Thus, the null hypothesis will be rejected at any of the three significance level.
Conclusion:
As the <em>p</em>-value is too small the null hypothesis will be rejected concluding that there is a higher proportion of people supporting the home team.