What is the rate of change?
1 answer:
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See in the explanation
<h2>Explanation:</h2><h2 /><h3>Part 1.</h3>If you have two variables, the proportional relationship tells us that the ratio between these variables stays the same. Suppose you have two variable , so in proportional relationship we say
varies proportionally as
or in other terms
is directly proportional to
. If so, then
increases as
increases or
decrases as
decreases:
But how does the slope relate to the equation? Well, in this case is the equation of a line and
which is the constant of proportionality represents the slope of the line.
Here we have:
The slope is the steepness of the line and also tells us its direction. But what do the graphs of lines given by that form have in common? Well, the common thing is that they all pass through the origin (0, 0), because the y-intercept is
On the other hand, how might they differ? Well, they might differ in the inclination. So we can measure this as:
- m > 0, the line increases its outputs if you move from left to right.
- m < 0, the line decreases its outputs if you move from left to right.
- m = 0, the line lies on the x-axis and is constant.
- m <em>undefined, </em>this occurs when the line is vertical.
The table shows relationship between time (s) and distance (m) of a train that is traveling. We know that the table represents a linear relationship because the between two consecutive outputs (distance) is constant, that is:
So, the equation of the line is:
a)
In this case, we have a relationship between a hiker's elevation and time given by a proportional relationship. We know this is so because the graph is a line and passes through the origin (See Part 2). So we can find the constant of proportionality by computing the slope of the line. Therefore:
So the slope is also:
b)
So the equation of the line can be written as:
As we said before, the graph of lines given by the form:
passes through the origin having slope . In this case, we have the following equation:
So we can graph this with two points, since the origin is a point that lies on the line, we just need another point. Let's say:
Graph a line that passes through these two points as shown below
<h3>Part 6.</h3>As the problem states, Resting heart rate is a measure of how fast the heart beats when a person is not performing a physical activity. So you can see that the graph shows the number of heartbeats over time for a given person. So we have the following equation of the slope in an incomplete form:
Since this line passes through the origin, then:
Here you have another example of proportional relationships. In this case, the number of gallons of white paint is related to the number of gallons of red paint. Since this line passes through the origin, we just need to find the slope in order to build up the equation of the line:
Finally, the equation of the line is:
His graph is incorrect. In fact, the graph comes from the equation:
Remember that we said above that if m < 0, the line decreases its outputs if you move from left to right.
In the graph occurs the opposite because the line increases its outputs if you move from left to right or, in other words, m > 0 and in this case m = 1, so:
Equation of lines: brainly.com/question/12169569
Proportional relationships: brainly.com/question/674693
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Tommy walks from his home at (0,0)
i.e Home is at H ( 0,0)
To the mall
Mall is at M (0, 6)
walks to a movie theater at
Theater , T( 5, 6)
Tommy walks to the store at
Store is at S (5,0)
Plot each coorinates on the graph :
each grid of square represent one block :
i.e. number of blcok from H to M = 5
Then number of bocks frm M to T is 6 blocks
Number of blocks fromT to S is 5 blocks
Number of blocks from S to H is 6
So total number if blocks are = 5 + 6 + 5 + 6
Number of blocks Tommy walks = 22 blocks
Answer : 22 blocks
