Challenge Decide whether the function is linear or nonlinear using both a table and a graph. Use pencil and paper. Find a linear function. Make a table and a graph for the function to explain why it is linear.

Question

y
=
−​(x
−3​)
2
−3
Question content area bottom
Part 1
Complete the table of values for the function.
x
y
1
enter your response here
2
enter your response here
3
enter your response here
4
enter your response here
5
enter your response here

Answer 1

x y
1 -4
2 -3
3 -2
4 -1
5 0

Part 2
Plot the points on a graph and determine if the function is linear.

By plotting the points (1,-4), (2,-3), (3,-2), (4,-1), and (5,0) on a graph, we can see that the points create a straight line. Therefore, the function is linear.

Part 3
Find a linear function for the given table and graph.

From the table and graph, we can see that the function has a constant rate of change. The rate of change is equal to 1 between any two points.

Using the point-slope form of a linear equation, with the point (2,-3), we can write the equation as:

y - y1 = m(x - x1)
y - (-3) = 1(x - 2)
y + 3 = x - 2
y = x - 5

Therefore, the linear function for this table and graph is y = x - 5.