Answers:

1. Sean tutors math students to earn extra money.

   • (a) $4 \, \text{hours} \times 20 \, \text{\$/hour} = 80 \, \text{\$}$
   • (b) Equation: $y = 20x$

2. Write an equation to convert inches to centimeters:

   • Equation: $y = 2.54x$

3. Write an equation of the line passing through the points (-5, -25), (0, 0), and (3, 15):

   • Slope $m = \frac{15 - 0}{3 - 0} = 5$
   • Equation: $y = 5x$

4. Caleb’s run graph:

   • (a) Four points: $(0, 0), (10, 4), (20, 8), (30, 12)$
   • (b) Slope $m = \frac{12 - 0}{30 - 0} = \frac{2}{5}$
   • (c) Equation: $y = \frac{2}{5}x$

5. Sketch the graph of $y = 4x$:

   • Key points: $(0, 0), (1, 4), (-1, -4), (2, 8), (-2, -8)$

6. Write an equation that models the relationship in the table:

   • Slope $m = \frac{-15 - (-9)}{20 - 12} = \frac{-6}{8} = -\frac{3}{4}$
   • Using $y - (-9) = -\frac{3}{4}(x - 12)$, simplify:
   • Equation: $y = -\frac{3}{4}x$

Let me know if you have questions or want detailed explanations.

5 Related Questions:

1. What would the slope be if Sean charged $30/hour?
2. Can you convert a measurement of 50 inches to centimeters using your equation?
3. What is the y-intercept of the line passing through (0, 0) and (3, 15)?
4. How does changing Caleb’s running speed affect the equation $y = \frac{2}{5}x$?
5. What happens to the graph of $y = 4x$ if you change it to $y = -4x$?

Tip:

To derive equations for straight lines, always identify the slope $m$ first using $m = \frac{y_2 - y_1}{x_2 - x_1}$.