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3 years ago

Which of the following represents the graph of the equation y = 1/2x?

Mathematics

1 answer:

Natasha_Volkova [10]3 years ago

8 0

Answer:

(B)

Step-by-step explanation:

Here's what we know about the equation:

- it's a positive equation

- the y-intercept is (0,0)

- the slope is 1/2

Because the equation is positive, this means the graph will increase up from left to right, so you can cross out answer choice A & D.

To find out if B or C has the right slope, you can either plug in points or use the rise/run method.

I'm going to use both methods to figure out which answer choice is correct:

<u>Plug in points method:</u>

Let's plug in the value 2 in to the equation y = 1/2x.

1/2 * 2 = 1

So at (1,2) the function should include that point.

Only B has (1,2), so that's your answer.

<u>Rise/run method:</u>

Rise/run is a method used to figure out the slope of a function or draw a function on a graph.

Rise corresponds to the numerator. In this case, 1.

Run corresponds to the denominator. In this case, 2.

We are going to start at (0,0) and go up 1 (rising 1 unit) and go 2 to the right (running 2 units). After this, we should arrive at a point on the graph.

Only answer choice B does this.

**Reminder: be careful, the each blue line on the graph ISN'T a whole number interval; it uses 1/2 intervals.

Hope that helps (●'◡'●)

You might be interested in

Use technology or a z-score table to answer the question.

Alik [6]

Answer:

The second choice: Approximately $65.2\%$ of the pretzel bags here will contain between 225 and 245 pretzels.

Step-by-step explanation:

This explanation uses a z-score table where each $z$ entry has two decimal places.

Let $\mu$ represent the mean of a normal distribution of variable $X$ . Let $\sigma$ be the standard deviation of the distribution. The z-score for the observation $x$ would be:

$\displaystyle z = \frac{x - \mu}{\sigma}$ .

In this question,

$\mu = 240$ .
$\sigma = 9.3$ .

Calculate the z-score for $x_1 = 225$ and $x_2 = 245$ . Keep in mind that each entry in the z-score table here has two decimal places. Hence, round the results below so that each contains at least two decimal places.

$\begin{aligned} z_1 &= \frac{x_1 - \mu}{\sigma} \\ &= \frac{225 - 240}{9.3} \approx -1.61\end{aligned}$ .

$\begin{aligned} z_2 &= \frac{x_2 - \mu}{\sigma} \\ &= \frac{245 - 240}{9.3} \approx 0.54\end{aligned}$ .

The question is asking for the probability $P(225 \le X \le 245)$ (where $X$ is between two values.) In this case, that's the same as $P(-1.61 \le Z \le 0.54)$ .

Keep in mind that the probabilities on many z-table correspond to probability of $P(Z \le z)$ (where $Z$ is no greater than one value.) Therefore, apply the identity $P(z_1 \le Z \le z_2) = P(Z \le z_2) - P(Z \le z_1)$ to rewrite $P(-1.61 \le Z \le 0.54)$ as the difference between two probabilities:

$P(-1.61 \le Z \le 0.54) = P(Z \le 0.54) - P(Z \le -1.61)$ .

Look up the z-table for $P(Z \le 0.54)$ and $P(Z \le -1.61)$ :

$P(Z \le 0.54)\approx 0.70540$ .
$P(Z \le -1.61) \approx 0.05370$ .

$\begin{aligned}& P(225 \le X \le 245) \\ &= P\left(\frac{225 - 240}{9.3} \le Z \le \frac{245 - 240}{9.3}\right)\\&\approx P(-1.61 \le Z \le 0.54) \\ &= P(Z \le 0.54) - P(Z \le -1.61)\\ &\approx 0.70540 - 0.05370 \\& \approx 0.65.2 \\ &= 65.2\% \end{aligned}$ .