Here's how to graph the line $y = -2x + 3$:

Step 1: Identify the slope and y-intercept

The equation is in slope-intercept form: $y = mx + b$, where:

• $m$ is the slope, and
• $b$ is the y-intercept (the point where the line crosses the y-axis).

For $y = -2x + 3$:

• The slope $m = -2$,
• The y-intercept $b = 3$.

Step 2: Plot the y-intercept

The y-intercept is $3$, so the line crosses the y-axis at the point $(0, 3)$. Start by plotting this point on the graph.

Step 3: Use the slope to find another point

The slope $-2$ means that for every 1 unit you move to the right on the x-axis, the line falls by 2 units on the y-axis. Starting from the point $(0, 3)$:

• Move 1 unit to the right (to $x = 1$),
• Move 2 units down (to $y = 1$).

Plot this second point at $(1, 1)$.

Step 4: Draw the line

Now that you have two points $(0, 3)$ and $(1, 1)$, draw a straight line passing through these points. This is the graph of the line $y = -2x + 3$.

Step 5: Extend the line

Continue the line in both directions (left and right) using the same slope. Make sure it extends across the graph, and label the points you used.

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Example:

1. Plot the point $(0, 3)$ on the graph.
2. From $(0, 3)$, move right by 1 unit and down by 2 units to reach $(1, 1)$.
3. Draw a straight line connecting these two points and extend it.

This will give you the graph of the line $y = -2x + 3$.

If you need more help or details, feel free to ask!

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Related Questions:

1. How do you determine the x-intercept of a line?
2. What is the difference between positive and negative slopes in terms of graphing?
3. How do you graph vertical and horizontal lines?
4. How can you graph a line using two points instead of slope-intercept form?
5. What are some strategies for accurately graphing lines without gridlines?

Tip:

When graphing, always start with the y-intercept, and then use the slope to find additional points. This helps ensure your line is accurate.