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.

Question

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