Determine a function equation for each table of values
(x,y) (10,0) (11,-5) (12,-10) (13,-15)
y changes by -5 when x changes by 1.
So, y = -5x + b
Surely you can find b, since you have already had Algebra I...
To determine a function equation for the given table of values, we need to identify the pattern or relationship between the independent variable (x) and the dependent variable (y).
Looking at the table, we notice that the x-values are increasing by 1 each time, while the y-values are decreasing by 5. This suggests that there is a linear relationship between x and y.
To find the equation of a linear function, we can use the slope-intercept form, which is given by:
y = mx + b
Here, m represents the slope of the line, and b represents the y-intercept.
Step 1: Calculate the slope (m):
To find the slope, we can choose any two points from the table and use the following formula:
m = (change in y) / (change in x)
Using the points (10,0) and (11,-5):
m = (-5 - 0) / (11 - 10)
m = -5 / 1
m = -5
Step 2: Determine the y-intercept (b):
To find the y-intercept, we can substitute the values of one of the points into the equation and solve for b.
Using the point (10,0):
0 = (-5)(10) + b
0 = -50 + b
b = 50
Step 3: Write the equation:
Now that we have the slope (m = -5) and the y-intercept (b = 50), we can write the equation of the linear function:
y = -5x + 50
Therefore, the function equation for the given table of values is y = -5x + 50.