Question

the table shows some corresponding x- and y- values of a linear function.
x]3/6/12/15
y]2/4/8/10


what is the slope of the graph

Answer 1

To find the slope of a linear function, you can use the formula for slope, which is given by:

\[
\text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1}
\]

You can choose any two points from the provided values. Let's take the points (3, 2) and (6, 4).

Using these points:
- \( (x_1, y_1) = (3, 2) \)
- \( (x_2, y_2) = (6, 4) \)

Now, substitute these values into the slope formula:

\[
m = \frac{4 - 2}{6 - 3} = \frac{2}{3}
\]

Therefore, the slope of the graph is \(\frac{2}{3}\).

You could also choose other pairs of points and the slope will remain the same, confirming that the function is linear. For instance, taking points (12, 8) and (15, 10):

\[
m = \frac{10 - 8}{15 - 12} = \frac{2}{3}
\]

The slope for any two points will consistently yield \( \frac{2}{3} \).