x0

Question

2

4

6

8

y-1-2-3-4-5

A) Do the values in the table above represent a linear function?

Yes, it represents a linear

く

B) If you said it's a linear function, justify your answer.

Because the x-values increase by 1 as the y-values decrease by 2

What is the slope of the line that goes through the points in the table?

m= *blank*

A 1/2
B -1
C 1
D 2
E -1/2
F -2

Also give me a y-Intercept

Answer 1

To determine if the values in the table represent a linear function, we can analyze the differences in the values.

A) Do the values in the table above represent a linear function?

Yes, it represents a linear function.

B) If you said it's a linear function, justify your answer.

The x-values (0, 2, 4, 6, 8) increase by 2 each time, while the corresponding y-values (-1, -2, -3, -4, -5) decrease by 1 each time. The consistent difference in the y-values as the x-values increase indicates a linear relationship.

To find the slope (m), we calculate the change in y divided by the change in x:

• Change in y: From -1 to -5, the change is -5 - (-1) = -4
• Change in x: From 0 to 8, the change is 8 - 0 = 8

Now, we can find the slope: \[ m = \frac{\Delta y}{\Delta x} = \frac{-4}{8} = -\frac{1}{2} \]

So, the slope is \( \mathbf{m = -\frac{1}{2}} \).

For the slope options:

E) \(-\frac{1}{2}\)

Y-Intercept

The y-intercept is the value of y when x = 0. From the table, when \( x = 0 \), \( y = -1 \).

Thus, the y-intercept is \( (0, -1) \).

In short, the slope is \(-\frac{1}{2}\) and the y-intercept is \(-1\).