Answer:
Step-by-step explanation:
In the linear function y = mx + b, m is the slope which is a constant among all the values in the table, and b is the y intercept. The y-intercept exists where x = 0.
Looking at the y values of our table, it appears that they are decreasing by a constant 1/2. If this is linear, then that's our slope: -1/2.
Now looking at the coordinate where x = 0, we see that y is 2.5. Again, if this is linear, our equation is
[tex]y=-\frac{1}{2}x+2.5[/tex]
Let's test it out. Let's plug in a 3 for x. If we solve and get that y = 1, then we know we have found the correct equation for the data:
[tex]y=-\frac{1}{2}(3)+2.5[/tex] which simplifies to
[tex]y=-\frac{3}{2}+2.5[/tex]
-3/2 is the same thing as -1.5 so
y = -1.5 + 2.5 so
y = 1
In our table, we see that when x = 3, y = 1. So we're good!
