Question

Use the table to answer the question.

Determining the linear equation based on given data points.
x y
11 58
20 103
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y= mx+b form.

(1 point)
y = __x + __

Answer 1

To find the linear equation in the form \( y = mx + b \), we need to determine the slope (\( m \)) and y-intercept (\( b \)) using the given points (11, 58) and (20, 103).

1. **Calculate the slope (m)**:
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, let \((x_1, y_1) = (11, 58)\) and \((x_2, y_2) = (20, 103)\):
\[
m = \frac{103 - 58}{20 - 11} = \frac{45}{9} = 5
\]

2. **Use the slope to find the y-intercept (b)**:
Now that we have the slope \( m = 5 \), we can use one of the points to solve for \( b \). We'll use the point (11, 58):
\[
y = mx + b
\]
\[
58 = 5(11) + b
\]
\[
58 = 55 + b
\]
\[
b = 58 - 55
\]
\[
b = 3
\]

3. **Write the equation**:
Substituting \( m \) and \( b \) back into the equation gives:
\[
y = 5x + 3
\]

Thus, the equation of the linear function that models the relationship shown in the table is:
\[
y = 5x + 3
\]

So the final answer is:
y = **5**x + **3**