Use the table of values.
x y
-2 -5
0 -1
1 1
2 3
A. Graph the ordered pairs.
B. Is the function linear? Explain.
C. Write a rule for the ordered pairs in terms of x and y.
D. What is the value of y when x = 10?
A. Can't graph for you, sorry!
B. The function is linear, as for every equal change in x, there is a set change in y.
C. x increases by 1 every time y increases by 2. (y=2x-1)
D. Plug into equation y=2x-1, so we get 20-1=19
A. Graph the ordered pairs:
To graph the ordered pairs, you would plot each point on a coordinate plane. The x-values are -2, 0, 1, and 2, and the corresponding y-values are -5, -1, 1, and 3. So, for (-2, -5), you would plot a point at x = -2 and y = -5; for (0, -1), you would plot a point at x = 0 and y = -1; for (1, 1), you would plot a point at x = 1 and y = 1; and for (2, 3), you would plot a point at x = 2 and y = 3. After plotting all the points, you can connect them to see the overall shape of the graph.
B. Is the function linear? Explain:
To determine if the function is linear, you need to check if the points on the graph line up in a straight line. From the values given, it appears that the plotted points do not form a straight line. Therefore, the function is not linear.
C. Write a rule for the ordered pairs in terms of x and y:
To find a rule for the ordered pairs, you need to see if there is a pattern in how x and y values relate to each other. Looking at the given values, we can observe that for every increase in x by 1, y increases by 2. So, the rule can be written as y = 2x - 1. This means that for any x-coordinate, if you multiply it by 2 and subtract 1, you will get the corresponding y-coordinate.
D. What is the value of y when x = 10?
To find the value of y when x = 10, you can substitute x = 10 into the rule we found in the previous step. So, y = 2(10) - 1.
Simplifying this, we get y = 20 - 1 = 19. Therefore, when x = 10, y = 19.