To graph the linear function [tex]\( y = 2x - 3 \)[/tex] using a graphing calculator, follow these steps:
1. Turn on your graphing calculator and make sure it is set to the graphing mode.
2. Enter the function [tex]\( y = 2x - 3 \)[/tex]:
- Locate the button labeled `Y=` or similar, which allows you to enter functions to graph.
- In the space provided, input the equation [tex]\( y = 2x - 3 \)[/tex]. This typically involves typing `2`, then `X`, then the minus sign `-`, and finally `3`.
3. Set the viewing window:
- Adjust your graphing window to be able to see a broad enough portion of the graph.
- For example, you might set the x-axis to range from -10 to 10 and the y-axis to range from -20 to 20. These settings ensure that you see where the graph crosses the axes and have a clear view of the trend of the line.
4. Graph the function:
- Once you have entered the function and set the viewing window, press `GRAPH` to display the graph on the screen.
- You should see a straight line that represents the equation [tex]\( y = 2x - 3 \)[/tex].
5. Analyze the graph:
- Identify key points of the graph. Since it is a linear function, you can find the slope and y-intercept directly from the equation:
- The slope [tex]\( m \)[/tex] is 2, which means the line rises 2 units for every 1 unit it moves to the right.
- The y-intercept is -3, which is the point where the line crosses the y-axis.
To summarize the graph:
- The line will cross the y-axis at [tex]\( (0, -3) \)[/tex].
- It will have a slope of 2, showing that for each step to the right (increase in [tex]\( x \)[/tex]), the value of [tex]\( y \)[/tex] increases by 2 units.
- The x-intercept can be calculated by setting [tex]\( y = 0 \)[/tex]:
[tex]\[
0 = 2x - 3 \Rightarrow 2x = 3 \Rightarrow x = \frac{3}{2} = 1.5
\][/tex]
So, the line will cross the x-axis at [tex]\( (1.5, 0) \)[/tex].
These steps should help you successfully graph the function [tex]\( y = 2x - 3 \)[/tex] and understand its characteristics.
