Answer:
A. f(x) = -3x -7
Explanation:
You want an equation for the linear function shown in the table.
Approach
There are several ways you can go at this. One of the simplest is to eliminate answer choices that can't work.
Evaluate
You notice that answer choices C and D have x-coefficients of 1/3 and -1/3. When you multiply any of the x-values from the table by these numbers, you will not get an integer. Since all of the added constants in the equations are integers, and all of the y-values in the table are integers, having a non-integer value cannot work. (This eliminates choices C and D.)
Evaluating the first two equations for x = -4, we get ...
- -3(-4) -7 = 12 -7 = 5
- -3(-4) +7 = 12 +7 = 19
The first of these matches the table value y=5, so the first equation is the only one that works.
A. f(x) = -3x -7
Find the equation
Another approach you can use is to find the equation for the table. Examining the table, we see that differences between x-values are not constant, but there is a pair with a difference of 1: (4, -19) and (5, -22). This pair makes it easy to see the slope of the line is ...
m = (y2 -y1)/(x2 -x1) = (-22 -(-19))/(5 -4) = -3/1 = -3
The y-intercept can be found from ...
b = y1 -mx1
b = -19 -(-3)(4) = -19 +12 = -7
Now, the equation y = mx +b is ...
y = -3x -7 . . . . . . . . matches choice A
Examine the table
The y-intercept of the equation is the value when x=0. Looking at the table values, you can see that x=0 will lie between (x, y) = (-2, -1) and (4, -19). In each case, the y-value is negative. This means the y-intercept will be negative. This eliminates choices B and D.
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Additional comment
The attachment shows the result of evaluating each of the equations for the first point in the table. The only result with y=5 is the first result.
You will notice that we could find the answer with virtually no math by looking at the table values and the offered answer choices. (The 1/3x and the +7 choices make no sense, leaving only one choice.)
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