To graph the equation $y = 2x - 5$, follow these steps:

1. Identify the slope and y-intercept:

   • The equation is in slope-intercept form $y = mx + b$, where:
     • $m = 2$ (slope)
     • $b = -5$ (y-intercept)

2. Plot the y-intercept:

   • The y-intercept is $-5$, so plot the point $(0, -5)$.

3. Use the slope to find another point:

   • The slope $m = 2$ means "rise 2, run 1" (go up 2 units, right 1 unit).
   • From $(0, -5)$, move up 2 and right 1 to get $(1, -3)$.

4. Draw the line:

   • Connect the points with a straight line extending in both directions.

Now, I will generate a graph of $y = 2x - 5$. numpy as np import matplotlib.pyplot as plt

Define the function y = 2x - 5

def f(x): return 2*x - 5

Generate x values

x = np.linspace(-5, 5, 100) y = f(x)

Plot the function

plt.figure(figsize=(6,6)) plt.axhline(0, color='black', linewidth=1) # X-axis plt.axvline(0, color='black', linewidth=1) # Y-axis plt.grid(True, linestyle='--', linewidth=0.5)

plt.plot(x, y, label=r"$y=2x-5$", color='blue') plt.scatter(0, -5, color='red', label="(0,-5) y-intercept") plt.scatter(1, -3, color='green', label="(1,-3) using slope")

Labels and title

plt.xlabel("x") plt.ylabel("y") plt.title("Graph of y = 2x - 5") plt.legend() plt.show()Here is the graph of $y = 2x - 5$. The red point represents the y-intercept $(0, -5)$, and the green point is found using the slope.

Would you like a step-by-step explanation of how to graph it manually?

Here are some related questions:

1. How do you find the slope of a linear equation?
2. How do you determine if two lines are parallel or perpendicular?
3. What is the difference between slope-intercept form and standard form?
4. How can you find the x-intercept of $y = 2x - 5$?
5. How do transformations affect the graph of a linear equation?

Tip: The y-intercept is always where the graph crosses the y-axis, so you can quickly plot it before using the slope.