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3 years ago

What is the equation of the line that passes through the points (0, 6) and (-3, 0) and is parallel to y = 2x + 5

Mathematics

2 answers:

Nat2105 [25]3 years ago

8 0

answer:

y=2x+6

solution:

Alright, since the line is PARALLEL, the slope will remain the same. let call the # we will add to that b (like the 5 in y=2x+5).

so the formula will be y=2x+b

to find be, we will plug in one of the ordered pairs

6=2(0)+b

6=0+b

b=6

So, our equation is y=2x+6

to check:

(-3,0)

0=2(-3)+6

0=-6+6

0=0

nataly862011 [7]3 years ago

7 0

Answer:

y = 2x + 6

Step-by-step explanation:

The equation for this is y=mx+b, m being for slope and b being the y-intercept.

The first and easiest way to figure out this first is by finding the slope. Now because you have the information that it needs to be parallel, it's very fast and simple. Parallel means that it has the same slope and the lines will never cross each other. So, since the slope for this is 2, the new line you will be making will also have a slope of 2.

EXTRA NOTE- if it were perpendicular, you'd want to do the opposite reciprocal. Instead of being 2, it'd be -1/2, but luckily we're just dealing with parallel.

Now we need to find what the y-intercept is. Since math basically has a formula for everything, you will be using y-y(1)= m(x-x(1)). Now that looks slightly confusing, but basically you will just plug your y value into the y(1) and x coordinate into x(1) to simplify into slope intercept form (don't forget your slope!). It's always easier to use positive numbers for this, so I'll be using the coordinates (0, 6) and plug it in.

REMEMBER- coordinates are (x, y). Don't get it mixed up!

1. Write out your equation: y - 6 = 2 ( x - 0 )

2. Distribute: y - 6 = 2x - 0

3. Add 6 to the other side to get into your slope intercept form: y = 2x + 6

And that's how you get your line. Hope this helped and made at least some sense. :)

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The third option: "A coordinate plane with a line passing through (0, negative 4) and (2, 0)."

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Answer:

Null hypothesis: $\mu \leq 8000$

Alternative hypothesis: $\mu > 8000$

$z=\frac{8300-8000}{\frac{1200}{\sqrt{64}}}=2$

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Step-by-step explanation:

1) Data given and notation

$\bar X=8300$ represent the sample mean

$\sigma=1200$ represent the population standard deviation

$n=64$ sample size

$\mu_o =800$ represent the value that we want to test

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

z would represent the statistic (variable of interest)

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

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 8000, the system of hypothesis are :

Null hypothesis: $\mu \leq 8000$

Alternative hypothesis: $\mu > 8000$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

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z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

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

$z=\frac{8300-8000}{\frac{1200}{\sqrt{64}}}=2$

4) P-value

Since is a one-side upper test the p value would given by:

$p_v =P(Z>2)=0.0228$

5) Conclusion

If we compare the p value and the significance level assumed, for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean is significantly higher than $8000.

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