Which equation describe the relation indicated by the table

The scatter plot you described shows several points scattered between 5 and 45 on the x-axis and 5 and 35 on the y-axis. To determine the relationship indicated by the scatter plot, we need to analyze the pattern formed by these points.

If the points on the scatter plot form a distinct pattern, it suggests there is a relationship between the variables being plotted. In this case, the plot shows points scattered throughout the given range, but without forming a clear pattern.

When we talk about correlation in a scatter plot, we are referring to how closely the points on the plot resemble a line or a curve. In specific, positive correlation means that as the x-values increase, the y-values also tend to increase. Negative correlation implies that as the x-values increase, the y-values tend to decrease. Constant correlation means the relationship between the x-values and y-values remains constant.

In the scatter plot you described, there is no clear pattern or trend that shows either a positive or negative correlation. The points seem randomly scattered without following a specific direction. Hence, the best phrase that describes the relationship indicated by this scatter plot is "no correlation" (option D).

To determine the relationship indicated by the scatter plot, we need to analyze the pattern of the data points. Depending on the direction of the pattern, we can determine if there is a positive correlation, negative correlation, or no correlation.

To clarify, a positive correlation indicates that as one variable increases, the other variable also increases. On the other hand, a negative correlation indicates that as one variable increases, the other variable decreases. No correlation suggests that there is no clear relationship between the two variables.

Here are the step-by-step instructions to find the relationship indicated by the scatter plot using the given options:

1. Examine the scatter plot: Look at the distribution of the data points on the graph.
2. Identify the general trend: Determine if the data points are generally moving in an upward or downward direction or if there is no clear pattern.
3. Consider outliers: Analyze if there are any outliers that are significantly different from the general trend.
4. Determine the relationship: Based on the general direction of the data points, determine which option (A, B, C, or D) best describes the relationship.

Now, without the actual scatter plot, I cannot directly observe the pattern. However, I can guide you through the process if you provide some details about the scatter plot or any specific data points.

- (1/2)x + 2

Solution:

1) Table

x    y

-2   3
0    2
4    0
6   -1

The first thing that you must probe is whether the relation is linear.

When the relation is linear the rate of change is constant.

The rate of change is Δy / Δx

2) Let's calculate that rate for all the points given:

x    y

-2   3
0    2 ---> Δx = 0 -(-2) = 2, Δy = 2 - 3 = - 1 => Δy / Δx = - 1/2
4    0 ---> Δx = 4 - 0 =4, Δy = 0 - 2 = -2 => Δy / Δx = -2/4 = - 1/2
6   -1 ---> Δx = 6 - 4 = 2, Δy = - 1 - 0 = -1 => Δy / Δx = - 1/2

So, we have shown that the relation is linear.

3) Now, you can use the equation of the line: y = mx + b, where m is the slope (rate of change Δy / Δx) and b is the y-intercept.

We already found m = -1/2

The y-intercept is the value of y when x = 0, which you can get from the table; b = 2.

Therefore the equation is: y = (-1/2)x + 2.

Forgive me if i’m wrong but it might be negative correlation or no correlation. i hope it helps!

Forgive me if i’m wrong but it might be negative correlation or no correlation. i hope it helps!

- (1/2)x + 2

Solution:

1) Table

x    y

-2   3
0    2
4    0
6   -1

The first thing that you must probe is whether the relation is linear.

When the relation is linear the rate of change is constant.

The rate of change is Δy / Δx

2) Let's calculate that rate for all the points given:

x    y

-2   3
0    2 ---> Δx = 0 -(-2) = 2, Δy = 2 - 3 = - 1 => Δy / Δx = - 1/2
4    0 ---> Δx = 4 - 0 =4, Δy = 0 - 2 = -2 => Δy / Δx = -2/4 = - 1/2
6   -1 ---> Δx = 6 - 4 = 2, Δy = - 1 - 0 = -1 => Δy / Δx = - 1/2

So, we have shown that the relation is linear.

3) Now, you can use the equation of the line: y = mx + b, where m is the slope (rate of change Δy / Δx) and b is the y-intercept.

We already found m = -1/2

The y-intercept is the value of y when x = 0, which you can get from the table; b = 2.

Therefore the equation is: y = (-1/2)x + 2.

The answer would be: a. y=4x+2 

In this question, the table is made from an equation that follows y=ax+b. To find the equation, it would be easier to use x=0 so you can exclude the a value and find the value of b. From the description, you can find that x=0 will result in y=2. Then if you put it into the equation:

 y=ax+b
 2=a(0)+b
b=2

Now we need to find the value of a. You can do this by inserting any value of x and y beside x=0. Let's try to use x=-2 and y=-6
 y=ax+b
 -6 =a(-2)+2
-6= -2a+2
-2a= -6-2
-2a=-8
a= -8/-2=4

The equation would be:
 y=4x+2