To find the slope-intercept form of the equation for the line based on the given points, we first need to identify the slope (m) and the y-intercept (b) from the points provided. The points (miles, cost) are:
- (0, 3)
- (1.5, 5)
- (2, 8)
- (3, 10.5)
- (4, 13)
Step 1: Find the slope (m)
The slope \( m \) can be calculated from two points using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's use the points (0, 3) and (4, 13):
\[ m = \frac{13 - 3}{4 - 0} = \frac{10}{4} = 2.5 \]
Step 2: Use the y-intercept (b)
From the point (0, 3), we can see that the y-intercept \( b \) is 3.
Step 3: Write the equation in slope-intercept form
The slope-intercept form of the equation is given by:
\[ y = mx + b \]
Substituting the values we found for \( m \) and \( b \):
\[ y = 2.5x + 3 \]
Conclusion
The slope-intercept form of the equation for the taxi ride cost is:
\[ y = 2.5x + 3 \]
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