I hope this helps out and that I have the correct answers.
1) First we would need to create an equation. We can do this by finding the slope and the y-intercept. The equation form for functions is f(x)=mx+f(0), m being the slope, x being the input, and f(0) as the y-intercept. Using the formula,
[tex] \frac{rise}{run} [/tex]
we can determine the slope. The line is going down by one and to the right once as well. Since this line is moving at a downwards angle, we can determine that it is negative. Therefore our slope is -1/1 or just -1. The y-intercept can be found by looking at a place on the graph where x is equal to 0. At the point, y is equal to 2. Therefore our y-intercept is (0,2) or just 2. Now we can make an equation. f(x)=-1x+2 or f(x)=-x+2. Now we use 2 as our input.
f(2)
We will now replace x with 2.
f(2)=-1(2)+2
We can solve.
f(2)=-2+2
First we multiply -1 and 2 to get -2.
f(2)=0
Lastly, we add.
In conclusion, when the input (x) is 2, the output (y) is 0.
Another, simpler, way to do this is to look at the graph and see the y value when x is 2.
2) Using the steps to write an equation that I showed above, we can find the slope and y-intercept. Since this is a table, not a graph, we can instead simply count the difference in the y values. For instance, between 6 and 3, we have 3. But since we are subtracting, it would be -3. Therefore our slope is -3. To find our y-intercept, we can look at the y value when x is 0. The output, or y, is 6 when x is 0. Therefore our y-intercept is (0,6) or 6. Our equation would be f(x)=-3x+6. To find out what the y value of 2 is, we replace x with 2.
f(2)
Replacing x with 2.
f(2)=-3(2)+6
Now we can multiply.
f(2)=-6+6
Add!
f(2)=0
In conclusion, when the input (x) is 2, the output (y) is 0.
Another, simpler, way to do this is to look at the table and see the y value when x is 2.
Thank you, and I apologize if this is not what you are looking for or is confusing or incorrect.
