The equation y = 8x + 12, where x is the number of hours and y is the total cost, represents what the surf instructor charges for lessons. Use this information to describe how to draw the line on a graph.
To draw the line on a graph using the equation y = 8x + 12, you would first draw the x-axis horizontally representing the number of hours (x) and the y-axis vertically representing the total cost (y).
Next, you need to find two points that lie on the line. You can determine these points by choosing any values for x and then substituting them into the equation to calculate the corresponding values for y.
For example, if you choose x = 0, then the equation becomes y = 8(0) + 12 which simplifies to y = 12. Thus, the first point is (0, 12).
If you choose another value, let's say x = 2, then the equation becomes y = 8(2) + 12 which simplifies to y = 16 + 12 = 28. Thus, the second point is (2, 28).
Once you have these two points, you can plot them on the graph. Start at the origin (0, 0) and then go 12 units up on the y-axis to plot the first point (0, 12). Then, from the first point, go 2 units to the right on the x-axis and 16 units up on the y-axis to plot the second point (2, 28).
Lastly, draw a straight line passing through these two points. The line represents the relationship between the number of hours and the total cost of the surf instructor's lessons.
To draw the line y = 8x + 12 on a graph, follow these steps:
1. Draw two perpendicular lines that intersect at a point, creating a coordinate plane. The horizontal line is the x-axis, and the vertical line is the y-axis.
2. Determine the range of values for x that you want to plot on the graph. For example, if you want to plot the line for x values ranging from 0 to 10, mark these values on the x-axis.
3. Substitute different values of x into the equation y = 8x + 12 to determine the corresponding y-values. For example, if x = 0, y = 8(0) + 12 = 12. If x = 1, y = 8(1) + 12 = 20. If x = 2, y = 8(2) + 12 = 28, and so on.
4. Plot the points (x, y) on the graph. For the example, plot the points (0, 12), (1, 20), (2, 28), and so on, until you have enough points to see a pattern.
5. Connect the plotted points with a straight line. The line should pass through each plotted point. If there is no pattern or the points do not align, double-check the equations and calculations.
6. Extend the line in both directions beyond the plotted points to indicate that the equation represents a continuous relationship between x and y.
The resulting line on the graph represents the surf instructor's charges for lessons based on the equation y = 8x + 12.