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3 years ago

What is an equation of the line that passing through the points (-2, -5) and (4, 7) ?

Mathematics

1 answer:

monitta3 years ago

6 0

Answer:

$y=2x-1$

Step-by-step explanation:

Use the slope-intercept formula: $y=mx+b$ where m is slope and b the y-intercept.

$(-2,-5)(4,7)$

Use the slope formula for when you have two points:

$\frac{y(2)-y(1)}{x(2)-x(1)}=\frac{rise}{run}$

Rise over run is the change in the y-axis over the change in the x-axis. Insert values:

$\frac{7-(-5)}{4-(-2)}$

Simplify parentheses (negative+negative=positive)

$\frac{7+5}{4+2}$

Simplify

$\frac{12}{6}=2$

2 is the slope:

$y=2x+b$

Now use one of the points to find the y-intercept by substituting the x and y values into the equation. Solve for b:

(4,7)

$y=2x+b\\7=2(4)+b$

$7=8+b\\7-8=8-8+b\\7-8=b\\-1=b\\b=-1$

The y-intercept is -1. Insert into the equation. Change the + symbol to -:

$y=2x-1$

Done.

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2 years ago

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3 years ago

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3 years ago

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An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 2 of 2 : S

ziro4ka [17]

Answer:

The 85% onfidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars is (0.151, 0.205).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

Sample of 421 new car buyers, 75 preferred foreign cars. So $n = 421, \pi = \frac{75}{421} = 0.178$

85% confidence level

So $\alpha = 0.15$ , z is the value of Z that has a pvalue of $1 - \frac{0.15}{2} = 0.925$ , so $Z = 1.44$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 - 1.44\sqrt{\frac{0.178*0.822}{421}} = 0.151$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.178 + 1.44\sqrt{\frac{0.178*0.822}{421}} = 0.205$

The 85% onfidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars is (0.151, 0.205).

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2 years ago