The tables of ordered pairs represent some point of the graph of linear functions f and g
x -2, 0, 2 x -2, 0, 2
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f(x) 1, 2, 3 g(x) 3, -5, -13
What is the system of equations for tables f(x) and g(x)
To find the equations of the lines representing the functions f(x) and g(x), we need to first determine the slope of each line using the data points given in the tables. The slope can be found by taking the vertical change (change in y or f(x)/g(x)) over the horizontal change (change in x) between two points.
For function f(x):
We can use any two points to find the slope (m). Let's take the points (-2, 1) and (2, 3).
The slope m for f(x) will be:
m = (change in f(x)) / (change in x)
m = (f(x2) - f(x1)) / (x2 - x1)
m = (3 - 1) / (2 - (-2))
m = 2 / 4
m = 1/2
Now, we will use one of the points to solve for the y-intercept (b). The point-slope form of the equation of a line is y - y1 = m(x - x1). Let's use the point (0, 2):
2 - y1 = (1/2)(0 - x1)
2 = (1/2)(0) + b
2 = b
Thus, the equation for f(x) is y = (1/2)x + 2 or f(x) = (1/2)x + 2.
For function g(x):
Again, we'll use any two points to find the slope. Let's take the points (-2, 3) and (2, -13).
The slope m for g(x) will be:
m = (change in g(x)) / (change in x)
m = (g(x2) - g(x1)) / (x2 - x1)
m = (-13 - 3) / (2 - (-2))
m = -16 / 4
m = -4
Now we will solve for the y-intercept (b). Again, the point-slope form is y - y1 = m(x - x1). Let's use the point (0, -5):
-5 - y1 = (-4)(0 - x1)
-5 = (-4)(0) + b
-5 = b
Thus, the equation for g(x) is y = -4x - 5 or g(x) = -4x - 5.
In summary, the system of equations for the tables f(x) and g(x) is:
f(x) = (1/2)x + 2
g(x) = -4x - 5