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3 years ago

Find the equation of the line passing through the given point and

Mathematics

1 answer:

kow [346]3 years ago

8 0

Answer:

y= x -2

Step-by-step explanation:

<u>Slope-intercept form:</u>

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

Given equation: y= x +4

This equation is already in the slope-intercept form, thus its slope can be found from the coefficient of x.

Slope= 1

$\textcolor{steelblue}{\text{Parallel lines have the same slope.}}$

Slope of unknown line= 1

Substitute the m= 1 into y= mx +c:

y= x +c

To find the value of c, substitute a pair of coordinates the line passes through into the equation.

When x= 5, y= 3,

3= 5 +c

c +5= 3

c= 3 -5

c= -2

Thus, the equation of the line is y= x -2.

You might be interested in

The perimeter formula for a rectangle is 2l + 2w, where l is the length and w is the width.

erastovalidia [21]

Answer:

Correct.

Step-by-step explanation:

This is the perimeter formula for a rectangle.

Perimeter is l + l + w + 2

p = 2l + 2w

8 0

3 years ago

Suppose your professor reports that across all of her classes over the past 10 years, she found a -0.63 correlation between numb

Aleonysh [2.5K]

Using correlation coefficients, it is found that the -0.63 correlation between number of absences and final exam score means that there is a strong negative correlation between number of absences and final exam score.

<h3>What is a correlation coefficient?</h3>

It is an index that measures correlation between two variables, assuming values between -1 and 1.

If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.

In this problem, the correlation is of -0.63, hence:

It means that that there is a strong negative correlation between number of absences and final exam score.

To learn more about correlation coefficients, you can take a look at brainly.com/question/25815006

4 0

2 years ago

Nearest ten thousand 384400

olga_2 [115]

Answer:

The nearest ten thousand is 80,000.

8 0

3 years ago

A quadratic function f is defined by /«) = (x - 7)(x + 3).

lesya692 [45]

Answer:

Step-by-step explanation:

The two x intercepts are

x - 7 = 0

x = 7

x + 3= 0

x = - 3

The y intercept is just - 7 * 3 = - 21

To prove this more formally

f(x) = (x - 7)(x + 3)

f(x) = x^2 - 7x + 3x - 21

f(x) = x^2 - 4x - 21

6 0

3 years ago

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine fo

Blizzard [7]

Answer:

$t=\frac{26.8-29.9}{\frac{2.7}{\sqrt{9}}}=-3.44$

$df=n-1=9-1=8$

$p_v =P(t_{(8)}$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and is not enough evidence to conclude that the claim is true.

Step-by-step explanation:

Data given

$\bar X=26.8$ represent the sample mean

$s=2.7$ represent the sample standard deviation

$n=9$ sample size

$\mu_o =29.9$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean exceed 29.9 or no, the system of hypothesis would be:

Null hypothesis: $\mu \geq 29.9$

Alternative hypothesis: $\mu < 29.9$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{26.8-29.9}{\frac{2.7}{\sqrt{9}}}=-3.44$

P-value

The degrees of freedom are given by:

$df=n-1=9-1=8$

Since is a one sided test the p value would be:

$p_v =P(t_{(8)}$

Conclusion

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and is not enough evidence to conclude that the claim is true.

6 0

4 years ago