Determine if the given graph of the function y= -2/5x + 3. Enter 1 for yes. Enter 2 for no (1 point)
(1) Yes
Use the table to answer the question
X Y
2 22
8 25
Determine the rate of change and the initial value of the linear function given here as a table of values. (1 point)
The rate of change is m= , and the initial value is b= .
To determine the rate of change, we use the formula:
m = (Y2 - Y1) / (X2 - X1)
Using the given values from the table:
m = (25 - 22) / (8 - 2)
m = 3 / 6
m = 1/2
The rate of change is 1/2.
To determine the initial value, we can choose any point from the table. Let's use the point (2, 22). The initial value is the value of y when x is 0.
So, b = y - mx = 22 - (1/2) * 2
b = 22 - 1
b = 21
The initial value is 21.
Therefore, the rate of change is m = 1/2 and the initial value is b = 21.
Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.
Linear Function 1: y = x + 8
Linear Function 2: (4, 10) , (2, 6)
Linear Function has the greater rate of change
To compare the rate of change of Linear Function 1 and Linear Function 2, we need to find the slope (rate of change) of each function.
For Linear Function 1, the slope is equal to the coefficient of x, which is 1. So, the rate of change for Linear Function 1 is 1.
For Linear Function 2, we can use the formula:
m = (Y2 - Y1) / (X2 - X1)
Using the given values (4, 10) and (2, 6):
m = (6 - 10) / (2 - 4)
m = -4 / -2
m = 2
The rate of change for Linear Function 2 is 2.
Therefore, Linear Function 2 has the greater rate of change.
To determine if the given graph of the function y = -2/5x + 3 is correct or not, you need to compare the given equation with the graph plotted on a set of axes.
Here's how to do it:
1. Understand the equation: The equation y = -2/5x + 3 is in slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept.
2. Identify the slope: In this equation, the slope is -2/5. It indicates that for every positive increase of 5 in the x-coordinate, the y-coordinate decreases by 2. The negative sign denotes that the line slopes downward from left to right.
3. Recognize the y-intercept: The y-intercept is 3. This means that the line crosses the y-axis at the point (0, 3).
4. Analyze the graph: Plot the y-intercept (0, 3) as a point on the graph. With the slope of -2/5, use this information to draw the line. Start at the y-intercept point and move right 5 units and down 2 units to plot the next point. Continue this pattern to get multiple points and connect them to form a line.
5. Compare the graph and equation: Once you have plotted the line, compare it to the given graph. Does the graph match the line that you plotted? If the graph matches the line represented by the equation y = -2/5x + 3, then enter 1 for yes. Otherwise, enter 2 for no.
By following these steps, you should be able to determine whether the graph shown matches the equation or not.