Question

the graph represents the cost of a taxi ride dependent upon the number of miles driven. write an equation in slope-intercept form. what values are needed to complete the equation.
the graph shows a line going from (0,3) to (1,5.5) to (2,8) to (3, 10.5) to (4,13)

Answer 1

To write the equation of the line in slope-intercept form (y = mx + b), you need to determine two key values: the slope (m) and the y-intercept (b).

### Step 1: Determine the Slope (m)
The slope (m) can be calculated using the formula:

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

Using the points (0, 3) and (1, 5.5):

- \(y_1 = 3\)
- \(y_2 = 5.5\)
- \(x_1 = 0\)
- \(x_2 = 1\)

Substituting these values into the formula:

\[
m = \frac{5.5 - 3}{1 - 0} = \frac{2.5}{1} = 2.5
\]

### Step 2: Determine the Y-Intercept (b)
The y-intercept (b) is the value of y when x = 0. From the coordinate (0, 3), we have:

\[
b = 3
\]

### Step 3: Write the Equation
Now that we have the slope (m = 2.5) and the y-intercept (b = 3), we can write the equation in slope-intercept form:

\[
y = 2.5x + 3
\]

### Summary
The final equation representing the cost of the taxi ride as a function of the number of miles driven is:

\[
y = 2.5x + 3
\]

### Values Needed to Complete the Equation:
- Slope (m): 2.5
- Y-intercept (b): 3