Question

d the equation of the linear function represented by the table below in slope-intercept form.
x y
11 99
22 1414
33 1919
44 2424

Answer 1

To find the equation of the linear function represented by the data in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).

First, let's analyze the data points in the table:

- (11, 99)
- (22, 1414)
- (33, 1919)
- (44, 2424)

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

The slope (m) can be calculated using two points from the table. We can choose any two points; let's use (11, 99) and (44, 2424).

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2424 - 99}{44 - 11} \]

Calculating this:

\[ m = \frac{2325}{33} = 70.4545 \]

For easier calculation, let's round \( m \) to \( 70.45 \).

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

Now we can use one of the points and the slope to find the y-intercept (b). Using the point (11, 99):

\[ y = mx + b \]
\[ 99 = 70.45(11) + b \]

Calculating \( 70.45 \times 11 \):

\[ 70.45 \times 11 = 775.95 \]

Now, substituting that back into the equation:

\[ 99 = 775.95 + b \]

To solve for \( b \):

\[ b = 99 - 775.95 \]
\[ b = -676.95 \]

### Step 3: Write the Equation in Slope-Intercept Form

Now that we have the slope and y-intercept, we can write the equation:

\[ y = 70.45x - 676.95 \]

This is the equation of the linear function in slope-intercept form based on the data provided.