To graph the equation $2x = y + 5$, we first need to rewrite it in a more familiar form, such as the slope-intercept form $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

Step 1: Isolate $y$ in the given equation

Starting with: $2x = y + 5$ Subtract 5 from both sides: $2x - 5 = y$ Now we have: $y = 2x - 5$

Step 2: Analyze the equation

The equation $y = 2x - 5$ is in slope-intercept form, where:

• The slope $m = 2$
• The y-intercept $b = -5$

This means the line passes through the point $(0, -5)$ on the y-axis and has a slope of 2, meaning for every 1 unit you move to the right along the x-axis, the line moves up by 2 units.

Step 3: Plot the line

1. Start by plotting the y-intercept $(0, -5)$ on the graph.
2. From this point, use the slope $m = 2$. For each step of 1 unit to the right along the x-axis, move up 2 units on the y-axis.
3. Draw a straight line through the points.

Would you like to see a graph of this line, or do you need help with something else related to it?

Follow-up questions:

1. What would happen to the graph if the equation were $y = -2x - 5$?
2. How does the graph change if we add a constant to the x-term (e.g., $y = 2(x - 3) - 5$)?
3. How do you graph the equation of a line when given two points, say $(1, 2)$ and $(3, 6)$?
4. How can we determine the equation of a line if we're given the slope and one point on the line?
5. How does changing the slope value affect the steepness of the line?

Tip:

When graphing a line, always start with the y-intercept and then use the slope to plot additional points. This makes it easier to get an accurate representation of the line.