Substitute x with 2.

What is the slope of the line parallel to the points (3,-7) and (-6,5)

GrogVix [38]

The slope of the line parallel to the points (3,-7) and (-6,5) is $-\frac{4}{3}$

<u>Solution:</u>

We have been given two points of a line, and we have been asked to find the slope of a line parallel to it.

The given points are: (3,-7) and (-6,5)

According to the definition of parallel lines, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

And this is only possible if the two lines have the same slope.

Let the slope of the line be denoted by ‘m’.

So, to find the slope of the line given to us we do the following:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ --- equation 1

Where y and x are coordinates of the points given to us.

Therefore substituting the values eq1 becomes:

$\begin{array}{l}{m=\frac{5-(-7)}{-6-3}} \\\\ {m=\frac{5+7}{-9}=\frac{12}{-9}=-\frac{4}{3}}\end{array}$

Therefore the slope of the line is $-\frac{4}{3}$ So by definition, the slope of a line parallel to this line will also have the slope $-\frac{4}{3}$

5 0

3 years ago

Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in thi

mamaluj [8]

Answer:

Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario?

First, calculate the rate of change (Slope, once it is a linear function):

I will take the points: $(0, 100)$ and $(1, 80)$

$m=\frac{\Delta y}{\Delta x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{100-80}{0-1}=-20$

Let's understand the graph!

This linear graph is about songs being downloaded in a period of 5 weeks.

In the beginning, we have 100 songs to be downloaded. As the weeks past, the number of songs remaining decreases, that's why the graph's slope is negative. In week 5, all songs were downloaded.

The initial value (100) represents the number of songs.

Part B: Write an equation in slope-intercept form to model the relationship between x and y.

The Slope-intercept form of linear equations is $y=mx+b$

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

In this case, we have

$y=-20x+100$

3 0

4 years ago

Read 2 more answers

The function that represents bruce’s elevation in feet over time in hours is an exponential function that starts at 1,505 feet.

wariber [46]

Answer:

<h3>The function for Bruce’s elevation is $f(x)=1505(6)^x$ and because b=6 that is greater than 0, it is an exponential growth function.</h3>

Step-by-step explanation:

We have given initial Bruce’s elevation = 1,505 feet.

We know, the exponential function $f(x)=a(b)^x$ , where a is the initial value, b is the growth factor and x is the exponent represents time in hours.

Each successive hour, his average elevation change for the hike becomes 6 times the previous hourly elevation change.

Therefore, initial value a=1505, growth factor b for exponential function $f(x)=a(b)^x$ is 6.

Now we can plug a=1505 and b=6 in $f(x)=a(b)^x$ , we get

$f(x)=1505(6)^x$

Also note, if b>0, it would be an exponential growth function.

<h3>Therefore, the function for Bruce’s elevation is $f(x)=1505(6)^x$ and because b=6 that is greater than 0, it is an exponential growth function.</h3>

5 0

4 years ago

A graph titled Calories in Strawberries. The x-axis shows the number of strawberries, numbered 1 to 9, and the y-axis shows the

seraphim [82]

From the equation y = 4x, each strawberry contains 4 calories.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the number of calories in x strawberries. Hence:

y - 0 = [(27 - 0)/(6.8 - 0)](x - 0)

y = 4x

From the equation y = 4x, each strawberry contains 4 calories.

Find out more on equation at: brainly.com/question/2972832

#SPJ1

4 0

2 years ago

What is 14% of 230? a.16.4 b.0.06 c.32.2 d.3220

Nina [5.8K]

<h2>Step-by-step explanation:</h2>

Use a proportion to solve your question.

8 0

4 years ago