All categories

2 years ago

What is the equation of the line on the graph? Write your answer in slope-intercept form. (y = mx + b)

Mathematics

1 answer:

Nikolay [14]2 years ago

5 0

Answer:

y= ⅔x -2

Step-by-step explanation:

<u>slope-intercept </u><u>form</u>

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

Two given coordinates: (-3, -4) and (6, 2)

$\boxed{slope = \frac{y1 - y2}{x1 - x2} }$

Slope

$= \frac{2 - ( - 4)}{6 - ( - 3)}$

$= \frac{2 + 4}{6 + 3}$

$= \frac{6}{9}$

$= \frac{2}{3}$

Substitute m= ⅔ into the equation:

y= ⅔x +b

From the graph, the y- intercept is -2 since the line cuts through the x-axis at (0, -2).

Alternatively, we can also substitute a pair of coordinates into the equation to find the value of b.

When x= 6, y= 2,

$2 = \frac{2}{3} (6) + b$

2= 4 +b

b= 2 -4

b= -2

Thus the equation of the line is y= ⅔x -2.

You might be interested in

Which value from the set {2, 3, 6, 7} makes 3x + 5 = 11 true?

monitta

Answer:

Step-by-step explanation:

3 x 2 = 6 + 5 = 11

Can i have brainllest

4 0

3 years ago

Read 2 more answers

A 99 ft length of wire is to be cut into 2 pieces, so that the longer piece is eight feet longer than six times the shorter piec

Serhud [2]

here's the solution,

let the length of shorter peice = x

then the lenght of longer peice = 6x + 8

now, we know that the sum of length of peices measures 99 feet,

So,

=》x + 6x + 8 = 99

=》7x = 91

=》x = 13

shorter piece length = 13 feet

longer peice length = 13 × 6 + 8 = 78 + 8 = 86 feet

5 0

3 years ago

3(x-2)5 simplified and tiles

BartSMP [9]

Answer:

Step-by-step explanation:

7 0

2 years ago

What is the value of x in the equation

seraphim [82]

1/3 x - 1/2 = 18 1/2
1/3 x = 19 (add 1/2 on the right side to 18 1/2)
x = 57 (multiply the reciprocal of 1/3 and that will be 3/1 or 3 to 19 to get x by itself)
So, the answer is x = 57 (d. 57)

6 0

3 years ago

The local oil changing business is very busy on Saturday mornings and is considering expanding. A national study of similar busi

eimsori [14]

Answer:

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

Step-by-step explanation:

Previous concepts and data given

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=4.2$ represent the sample mean

$s=1.4$ represent the sample standard deviation

n=16 represent the sample selected

$\alpha=0.05$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is different from 3.6, the system of hypothesis would be:

Null hypothesis: $\mu = 3.6$

Alternative hypothesis: $\mu \neq 3.6$

If we analyze the size for the sample is < 30 and we know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

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

t-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".

Calculate the statistic

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

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Critical values

On this case since we have a bilateral test we need to critical values. We need to use the t distribution with $df=n-1=16-1=15$ degrees of freedom. The value for $\alpha=0.05$ and $\alpha/2=0.025$ so we need to find on the t distribution with 15 degrees of freedom two values that accumulates 0.025 of the ara on each tail. We can use the following excel codes:

"=T.INV(0.025,15)" "=T.INV(1-0.025,15)"

And we got $t_{crit}=\pm 2.131$

So the decision on this case would be:

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

Conclusion

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

3 0

3 years ago