Question

Find the slope and y-intercept using the table

X -3 -2 -1
Y 16 7 -2

The slope is *blank*

The y-intercept is *blank*


Use the options bellow


A (-11,0)

B (0,-11)

C -1/9

D (-1,-2)

E 9

F 1/9

G -9

H (11,0)

Answer 1

To find the slope (m) and the y-intercept (b) using the given points from the table, we can first identify the points from the table:

- When \( x = -3 \), \( y = 16 \) (Point 1: \((-3, 16)\))
- When \( x = -2 \), \( y = 7 \) (Point 2: \((-2, 7)\))
- When \( x = -1 \), \( y = -2 \) (Point 3: \((-1, -2)\))

1. **Calculate the slope (m)**:

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Let's use the first two points \((-3, 16)\) and \((-2, 7)\):

\[
m = \frac{7 - 16}{-2 - (-3)} = \frac{-9}{1} = -9
\]

So, the slope is \(-9\).

2. **Find the y-intercept (b)**:

We can use the slope-intercept form \(y = mx + b\). We can use one of the points and the slope to solve for \(b\). Let's use the point \((-2, 7)\):

\[
y = mx + b
\]
\[
7 = -9(-2) + b
\]
\[
7 = 18 + b
\]
\[
b = 7 - 18
\]
\[
b = -11
\]

So, the y-intercept is \(-11\).

3. **Final Answers**:

- The slope is **-9**.
- The y-intercept is **-11**.

Based on the options given:

- The slope is **G -9**.
- The y-intercept is **B (0,-11)**.