Question

Find the equation of the linear function represented by the table below in slope-intercept form. x y 11 00 22 minus, 1−1 33 minus, 2−2 44 minus, 3−3

Answer 1

To find the equation of the linear function in slope-intercept form, we first need to identify the slope and the y-intercept from the provided points in the table.

The points given in the table are:
- (11, 0)
- (22, -1)
- (33, -2)
- (44, -3)

### Step 1: Calculate the slope (m)

We can choose any two points to calculate the slope. Let’s use the points (11, 0) and (22, -1).

Using the slope formula:

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

Substituting the points:
- \( (x_1, y_1) = (11, 0) \)
- \( (x_2, y_2) = (22, -1) \)

So, we have:

\[
m = \frac{-1 - 0}{22 - 11} = \frac{-1}{11}
\]

### Step 2: Use one point to find the y-intercept (b)

Now, we can use one of the points (for example, (11, 0)) and the slope to find the y-intercept in the slope-intercept form \( y = mx + b \).

Using the point (11, 0):
\[
0 = \left(-\frac{1}{11}\right)(11) + b
\]

This simplifies to:
\[
0 = -1 + b \implies b = 1
\]

### Step 3: Write the equation

Now we have the slope \( m = -\frac{1}{11} \) and the y-intercept \( b = 1 \).

Thus, the equation in slope-intercept form is:
\[
y = -\frac{1}{11}x + 1
\]

So, the equation of the linear function is:
\[
\boxed{y = -\frac{1}{11}x + 1}
\]