Certainly! Graphing the linear equation y = 2x - 7 involves plotting points on the Cartesian plane and drawing a straight line through them. To graph this function, you can follow these steps:
1. **Create a Table of Values:** Start by choosing several values of 'x' and use the equation to find the corresponding values of 'y'. For a linear equation, two points are enough to define the line, but it's often helpful to use more to confirm the accuracy of your graph.
2. **Calculate the Corresponding 'y' Values:**
- When x = 0: y = 2(0) - 7 = -7
- When x = 1: y = 2(1) - 7 = -5
- Choose another value for x, maybe x = -1: y = 2(-1) - 7 = -9
(You may choose any other values of x as you wish to get more points on the line)
3. **Plot the Points on the Graph:**
- For x = 0, y = -7: Place a point at (0, -7) on the Cartesian plane.
- For x = 1, y = -5: Place a point at (1, -5) on the Cartesian plane.
- For x = -1, y = -9: Place a point at (-1, -9) on the Cartesian plane.
4. **Draw the Line:**
- Using a ruler, draw a straight line that passes through the points you plotted. Because y = 2x - 7 is a linear equation, the graph should be a straight line, and all the points you computed should lie on this line.
5. **Extend the Line and Label:**
- Extend the line across the graph in both the positive and negative directions.
- Mark the line with the equation y = 2x - 7, so anyone looking at the graph knows what function you've graphed.
6. **Add the axes Labels:**
- Label the horizontal axis as 'x' and the vertical axis as 'y'.
7. **Identify the Intercept Points:**
- The y-intercept is the point where the line crosses the y-axis. For the equation y = 2x - 7, the y-intercept is at (0, -7).
- The x-intercept is where the line crosses the x-axis. To find this, set y = 0 and solve for x: 0 = 2x - 7 which gives x = 7/2 = 3.5. Thus, the x-intercept is at (3.5, 0). Plot this point on the graph as well.
After you've completed these steps, you should have a straight line passing through the points you've calculated, properly labeled, which accurately represents the graph of y = 2x - 7.