Question

Find the slope and y intercept of the functions shown in the table

X 0 5
Y 1 -9

The slope is *blank*

The y intercept is *blank*

A (1,0)

B 2

C -2

D -1/2

E (2,0)

F 1/2

G (0, 1)

Answer 1

To find the slope and y-intercept of the linear function represented by the points from the table, we can use the given points \( (0, 1) \) and \( (5, -9) \).

1. **Calculating the slope (m)**:
The slope formula is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (x_1, y_1) = (0, 1) \) and \( (x_2, y_2) = (5, -9) \):

\[
m = \frac{-9 - 1}{5 - 0} = \frac{-10}{5} = -2
\]

2. **Finding the y-intercept (b)**:
The y-intercept occurs where \( x = 0 \). From the points provided, we can see that at \( x = 0 \), \( y = 1 \). Therefore, the y-intercept is:

\[
b = 1
\]

Now we can summarize our findings:

- The slope is \( -2 \).
- The y-intercept is \( 1 \).

Thus, filling the blanks:

The slope is **-2**.

The y-intercept is **1**.