Q1. The height y (in feet) of a movable bridge after rising for x seconds is represented by the equation y = 3x + 16. Graph the equation.

Background

Topic: Graphing Linear Equations

This question tests your understanding of how to graph a linear equation in slope-intercept form, which is a foundational concept in college algebra. The equation models a real-world scenario where the height of a bridge increases over time.

Key Terms and Formulas

• Slope-intercept form:

• Slope (m): The rate of change; here, (the bridge rises 3 feet per second).

• y-intercept (b): The starting value when ; here, (the initial height of the bridge).

Step-by-Step Guidance

1. Identify the slope and y-intercept from the equation . Here, the slope and the y-intercept .

2. Plot the y-intercept on the graph. This is the point , where the bridge starts at 16 feet when seconds.

3. Use the slope to find another point. Since the slope is 3, for every 1 unit you move to the right (increase by 1), move up 3 units (increase by 3). So, from , the next point is .

4. Draw a straight line through these points to represent the equation. Extend the line in both directions, making sure it follows the pattern set by the slope.

Try solving on your own before revealing the answer!