The problem in the image asks to graph the line given by the equation:

$y = 3x - 5$

To help you plot the graph, we can calculate a few points by substituting different values of $x$ into the equation to find corresponding values of $y$. Let's calculate some pairs of $(x, y)$ values.

1. For $x = 0$: $y = 3(0) - 5 = -5$ So, $(0, -5)$ is one point.

2. For $x = 2$: $y = 3(2) - 5 = 6 - 5 = 1$ So, $(2, 1)$ is another point.

3. For $x = -1$: $y = 3(-1) - 5 = -3 - 5 = -8$ So, $(-1, -8)$ is another point.

4. For $x = 3$: $y = 3(3) - 5 = 9 - 5 = 4$ So, $(3, 4)$ is another point.

Now you can plot these points on the given coordinate plane:

• $(0, -5)$
• $(2, 1)$
• $(-1, -8)$
• $(3, 4)$

Connect the points with a straight line to form the graph of the equation.

Would you like a further detailed explanation, or do you have any questions?

Here are 5 related questions to deepen your understanding:

1. What is the slope of the line, and how does it affect the graph?
2. How would the graph change if the equation was $y = 3x + 5$ instead?
3. How can you determine the x-intercept of the line?
4. What is the significance of the y-intercept in the equation $y = 3x - 5$?
5. How would you graph the line if given the equation in a different form, such as $y - 1 = 3(x - 2)$?

Tip: The slope of a line represents how steep the line is, and it is found by calculating the change in $y$ divided by the change in $x$.