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

Step-by-Step Explanation:

1. Identify the slope and y-intercept:

   • The equation is in slope-intercept form, $y = mx + b$, where:
     • $m = 2$ (the slope), which means the line rises 2 units for every 1 unit it moves to the right.
     • $b = -5$ (the y-intercept), which is the point where the line crosses the y-axis.

2. Plot the y-intercept:

   • The y-intercept is $(0, -5)$. This is the first point to plot on the graph. On the graph, locate 0 on the x-axis and go down to -5 on the y-axis.

3. Use the slope to find another point:

   • The slope $m = 2$ is written as $\frac{2}{1}$. Starting from the point $(0, -5)$, move 1 unit to the right (along the x-axis) and 2 units up (along the y-axis). This gives you a new point at $(1, -3)$.

4. Plot more points (optional):

   • To ensure accuracy, you can use the slope to find more points. From $(1, -3)$, move another 1 unit to the right and 2 units up, which brings you to $(2, -1)$.

5. Draw the line:

   • Once you have at least two points (preferably more), draw a straight line through them.

Visual Verification:

If you'd like, I can help you with a digital sketch of the line based on the graph shown in your image. Does this solution make sense, or would you like me to provide more details or corrections?

Related Questions:

1. How do you calculate the slope of a line given two points?
2. What is the significance of the y-intercept in a linear equation?
3. Can you convert a line equation from standard form to slope-intercept form?
4. How do you find the x-intercept of a line?
5. How would you graph a line with a negative slope?

Tip: Always remember that the slope describes the direction and steepness of a line.