How do you graph a function like y=2x+0.5 and y=0.5x+1?
To graph a linear function like y = mx + b, where m is the slope and b is the y-intercept, you can follow these steps:
1. First, recognize the slope-intercept form of the equation, y = mx + b. Here, m represents the slope, which determines the steepness of the line, and b represents the y-intercept, which is the point where the line crosses the y-axis.
2. Start by plotting the y-intercept, which is the point (0, b). In the case of y = 2x + 0.5, the y-intercept is (0, 0.5), and for y = 0.5x + 1, it is (0, 1). Mark these points on the graph.
3. Next, calculate and plot additional points using the slope. The slope determines how much you move vertically (y-direction) for every unit you move horizontally (x-direction). For instance, in y = 2x + 0.5, the slope is 2, meaning that for every unit you move to the right, you move up by 2 units. Similarly, in y = 0.5x + 1, the slope is 0.5, meaning for every unit you move to the right, you move up by 0.5 units.
4. To calculate additional points, choose any x-value (except the one you already used for the y-intercept) and substitute it into the equation to find the corresponding y-value. For example, for y = 2x + 0.5, you can choose x = 1. Substitute it into the equation: y = 2(1) + 0.5. Solve it to find that y = 2.5. So, the point (1, 2.5) also lies on the line. Repeat this process to find more points if needed.
5. Plot the additional points on the graph and draw a straight line passing through all the points. Make sure that the line is straight and extends in both directions.
Here is an example graph of y = 2x + 0.5 and y = 0.5x + 1:
