Answer:
[tex] y = -2x [/tex]
Step-by-step explanation:
The given ordered pairs [tex](0,0), (1,-2), (2,-4), (3,-6), (4,-8)[/tex] represent a linear function.
To find the rule that represents the function, let's examine the pattern in the ordered pairs.
Notice that the y-coordinate is decreasing by 2 for every increase of 1 in the x-coordinate. This indicates that the slope of the line is -2.
Using the slope-intercept form of a linear equation, which is:
[tex] y = mx + b [/tex],
where
we can now find the equation.
We already know that the slope [tex] m = -2 [/tex].
Now, let's find the y-intercept by substituting one of the points into the equation.
We can use the point [tex](0,0)[/tex]:
[tex] 0 = -2(0) + b [/tex]
[tex] b = 0 [/tex]
So, the y-intercept [tex] b = 0 [/tex].
Therefore, the rule that represents the function is:
[tex] y = -2x [/tex]
