USING TABLES RULES AND GRAPHS QUIZ PART 2 (🚨PLS HELP🚨)
Find the function rule
x (-2) (-1) (0) (1) (2)
y (9) (4) (-1) (-6) (-11)
QUICK‼️‼️
To find the function rule, we need to observe the relationship between the x-values and the corresponding y-values.
By examining the given table:
x | y
---------
-2 | 9
-1 | 4
0 | -1
1 | -6
2 | -11
We notice that as the x-values increase by 1 unit, the y-values decrease by 5 units. This indicates a linear relationship between x and y.
To find the function rule, we can determine the constant rate of change or slope. The slope can be calculated using any pair of points from the table. Let's use the points (0, -1) and (1, -6):
slope = (change in y) / (change in x)
= (-6 - (-1)) / (1 - 0)
= -5 / 1
= -5
Now that we have the slope (-5), we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (0, -1), we substitute the values:
y - (-1) = -5(x - 0)
y + 1 = -5x
Finally, we rearrange the equation to get the function rule in slope-intercept form (y = mx + b):
y = -5x - 1
So, the function rule for the given table is y = -5x - 1.
To find the function rule that relates the values of x and y, we need to look for a pattern between the two sets of values.
Looking at the x-values, we can see that they are decreasing by 1 each time (from -2 to 2).
Looking at the y-values, we can see that they are decreasing by 5 each time (from 9 to -11).
Based on this pattern, we can deduce that the function rule is a linear equation of the form y = mx + b, where m represents the slope (change in y/change in x) and b represents the y-intercept (the value of y when x = 0).
To find the slope (m), we can choose two points from the table and calculate the change in y divided by the change in x.
Let's choose the points (-2, 9) and (0, -1):
m = (change in y) / (change in x) = (-1 - 9) / (0 - (-2)) = -10 / 2 = -5
So, the slope (m) is -5.
To find the y-intercept (b), we can substitute any point from the table into the equation y = mx + b and solve for b.
Let's choose the point (0, -1):
-1 = -5(0) + b
-1 = 0 + b
b = -1
Therefore, the y-intercept (b) is -1.
Putting it all together, the function rule that relates x and y is:
y = -5x - 1