Question

Find the slope of the linear function.

x | y
-2 | 16
0 | 21
2 | 26
4 | 31

Answer 1

Now what is the y- intercept?

Answer 2

To find the slope of a linear function given points, you can use the formula for the slope \( m \):

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

You can choose any two points from the table. Let's use the points (0, 21) and (2, 26):

1. Assign the points as follows:
- \( (x_1, y_1) = (0, 21) \)
- \( (x_2, y_2) = (2, 26) \)

2. Plug the values into the slope formula:

\[
m = \frac{26 - 21}{2 - 0} = \frac{5}{2}
\]

Thus, the slope of the linear function is \( \frac{5}{2} \). You can verify by calculating the slope using other pairs of points, and you should arrive at the same result.

Answer 3

To find the y-intercept of the linear function, we can use the general equation of a linear function in slope-intercept form, which is:

\[
y = mx + b
\]

Here, \(m\) is the slope and \(b\) is the y-intercept. We already calculated the slope \(m = \frac{5}{2}\).

Using one of the points from the table, we can substitute the \(x\) and \(y\) values to solve for \(b\). Let's use the point (0, 21):

1. Substitute \(x = 0\) and \(y = 21\) into the equation:

\[
21 = \frac{5}{2}(0) + b
\]

2. This simplifies to:

\[
21 = 0 + b
\]

Thus, \(b = 21\).

The y-intercept of the linear function is \(21\). In summary, the equation for the linear function is:

\[
y = \frac{5}{2}x + 21
\]