x y

-2 -5
0 -1
1 1
2 3

A. Graph the ordered pairs.



B. Is the function linear? Explain.

C. Write a rule for the ordered pairs in terms of x and y.

D. What is the value of y when x = 10?

B. does it have constant slope?

(-1+5)/(0+2) = 4/2 = 2
((1+1)/(1-0) = 2/1 = 2
(3-1)/(2-1) = 2/1 = 2
:)
slope, m = 2)

C. y = mx + b
so y = 2x-1

D. y = 2(10)-1 = 19

A. To graph the ordered pairs, plot each point on a coordinate plane. The x-coordinate corresponds to the horizontal axis, and the y-coordinate corresponds to the vertical axis.

For (-2, -5), plot a point at (-2, -5).
For (0, -1), plot a point at (0, -1).
For (1, 1), plot a point at (1, 1).
For (2, 3), plot a point at (2, 3).

Connect the points with a straight line to trace the graph.

B. To determine if the function is linear, we need to check if the graph is a straight line. If the graph is a straight line, then the function is linear.

Looking at the graph, it appears that the points are connected by a straight line. Therefore, the function is linear.

C. To write a rule for the ordered pairs in terms of x and y, we need to analyze the pattern.

From the given points, we can see that as x increases by 1, y increases by a constant amount. This suggests that the relationship between x and y is a linear one with a constant slope.

To find the slope, we can choose any two points from the given data. Let's use (-2, -5) and (0, -1):

Slope (m) = (change in y) / (change in x) = (-1 - (-5)) / (0 - (-2)) = 4 / 2 = 2

Now that we know the slope, we can use the point-slope form of a linear equation to write the rule:

y - y₁ = m(x - x₁), where (x₁, y₁) is any point on the line and m is the slope.

Using the point (0, -1):

y - (-1) = 2(x - 0)
y + 1 = 2x

So the rule for the ordered pairs is y = 2x - 1.

D. To find the value of y when x = 10, we can substitute x = 10 into the rule we just found and solve for y.

y = 2x - 1
y = 2(10) - 1
y = 20 - 1
y = 19

Therefore, when x = 10, y is equal to 19.