Question

find slope of the table
x:3,8,17
y:-4,11,38

Answer 1

To find the slope of the line represented by the points in the table, we can use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

We can use any two points from the table. Let's use the first two points: \((3, -4)\) and \((8, 11)\).

Here:
- \(x_1 = 3\)
- \(y_1 = -4\)
- \(x_2 = 8\)
- \(y_2 = 11\)

Now, substitute these values into the slope formula:

\[
m = \frac{11 - (-4)}{8 - 3} = \frac{11 + 4}{8 - 3} = \frac{15}{5} = 3
\]

Next, let's check the slope between the second and third points: \((8, 11)\) and \((17, 38)\).

Here:
- \(x_1 = 8\)
- \(y_1 = 11\)
- \(x_2 = 17\)
- \(y_2 = 38\)

Substituting these values into the slope formula:

\[
m = \frac{38 - 11}{17 - 8} = \frac{27}{9} = 3
\]

Finally, let's check the slope between the first and third points: \((3, -4)\) and \((17, 38)\).

Here:
- \(x_1 = 3\)
- \(y_1 = -4\)
- \(x_2 = 17\)
- \(y_2 = 38\)

Substituting these values into the slope formula:

\[
m = \frac{38 - (-4)}{17 - 3} = \frac{38 + 4}{17 - 3} = \frac{42}{14} = 3
\]

In all cases, the slope \( m \) is the same:

\[
\text{slope} = 3
\]

So, the slope of the line represented by the points in the table is **3**.