Question

Find the slope and y-intercept of the functions shown in the table and graph.
Graph:
x: -3, -2, -1
y: 16, 7, -2

Answer 1

To find the slope (m) and the y-intercept (b) of the function represented by the points in the table, we can use the following formula for the slope:

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

We can use any two points from the table. Let's pick the points (-3, 16) and (-1, -2).

- For point 1: \( (x_1, y_1) = (-3, 16) \)
- For point 2: \( (x_2, y_2) = (-1, -2) \)

Now plug in these values into the slope formula:

\[
m = \frac{-2 - 16}{-1 - (-3)} = \frac{-18}{-1 + 3} = \frac{-18}{2} = -9
\]

Now that we have the slope, we can use one of the points to find the y-intercept (b). The slope-intercept form of a linear equation is:

\[
y = mx + b
\]

Using the slope \( m = -9 \) and the point (-3, 16):

\[
16 = -9(-3) + b
\]
\[
16 = 27 + b
\]
\[
b = 16 - 27 = -11
\]

Thus, the slope of the line is \(-9\) and the y-intercept is \(-11\).

**Final Answer:**
- Slope (m): \(-9\)
- Y-intercept (b): \(-11\)