Understanding the equation y = 3x + 16 reveals the bridge's height (y) and time (x) relationship. Graphically, starting at (0, 16), with a slope of 3, the bridge rises steadily. Solving for x when y = 76 yields 20 seconds—verified on the graph at (20, 76).
Understanding the Equation:
The equation y = 3x + 16 represents the relationship between the height of the bridge (y) and the time it has been rising (x in seconds).
The slope, 3, indicates how much the height changes per second. In this case, the bridge rises 3 feet every second.
The y-intercept, 16, represents the initial height of the bridge when it starts rising.
2. Graphing the Equation:
Plot the y-intercept: Start by plotting the point (0, 16) on the graph, as this is where the bridge starts rising.
Use the slope to find more points: Since the slope is 3, for every increase of 1 in x (1 second), y increases by 3 (3 feet). This means you can plot points like (1, 19), (2, 22), (3, 25), and so on.
Connect the points: Draw a straight line through the plotted points to represent the bridge's height as it rises over time.
3. Finding the Time to Reach 76 Feet:
Substitute 76 for y: In the equation y = 3x + 16, replace y with 76 and solve for x: 76 = 3x + 16 60 = 3x x = 20
Interpret the result: This means it will take 20 seconds for the bridge to reach a height of 76 feet. You can also confirm this by looking at the graph and seeing that the point (20, 76) lies on the line.
Complete question:
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.