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)
The slope-intercept form of the equation for the line is y = _x + _

Answer 1

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

Step 1: Find the slope (m)

The slope can be calculated using two points on the line. You can take any two points; I'll use (0, 3) and (1, 5.5) for this example.

The formula for slope (m) is:

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

Substituting the values:

• Point 1: (0, 3) → \( (x_1, y_1) = (0, 3) \)
• Point 2: (1, 5.5) → \( (x_2, y_2) = (1, 5.5) \)

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

Step 2: Find the y-intercept (b)

The y-intercept (b) is the value of y when x = 0. From the point (0, 3), we see that the y-intercept \( b = 3 \).

Step 3: Write the equation

Now that we have both the slope and y-intercept, we can substitute them into the slope-intercept form \( y = mx + b \):

\[ y = 2.5x + 3 \]

Final Equation

So, the complete equation in slope-intercept form is:

\[ y = 2.5x + 3 \]

Summary

• Slope (m) = 2.5
• y-intercept (b) = 3

Thus, \(\text{Slope-Intercept Form: } y = 2.5x + 3\)