Question

Find the slope and y-intercept of the functions shown in the table.
x: 0, 5
y: 1,9

Answer 1

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

### Step 1: Find the Slope (m)

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

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

Substituting the coordinates of the points (0, 1) and (5, 9):

- \( x_1 = 0, y_1 = 1 \)
- \( x_2 = 5, y_2 = 9 \)

Now we compute the slope:

\[
m = \frac{9 - 1}{5 - 0} = \frac{8}{5}
\]

### Step 2: Find the y-intercept (b)

The y-intercept is the value of \( y \) when \( x = 0 \). From the table, we can see that:

When \( x = 0 \), \( y = 1 \).

Thus, the y-intercept \( b \) is:

\[
b = 1
\]

### Final Result

Now we can summarize our findings:

- **Slope (m)**: \(\frac{8}{5}\)
- **y-intercept (b)**: \(1\)

### Equation of the line

Using the slope-intercept form of a line, \( y = mx + b \):

\[
y = \frac{8}{5}x + 1
\]