Graph the line with the equation y = -3x + 3.
Understand the Problem
The question is asking how to graph the line represented by the equation y = -3x + 3. To do this, we can identify the slope and y-intercept, and then plot points on the graph accordingly.
Answer
The graph of the line is a straight line passing through points $(0, 3)$ and $(1, 0)$.
Answer for screen readers
The graph of the line $y = -3x + 3$ is a straight line passing through the points (0, 3) and (1, 0).
Steps to Solve
- Identify the slope and y-intercept
The equation is in the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Here, the slope $m = -3$ and the y-intercept $b = 3$.
- Plot the y-intercept
The y-intercept occurs when $x = 0$. For the given equation, substitute $x = 0$: $$ y = -3(0) + 3 = 3 $$ This point is (0, 3). Plot this point on the y-axis at $y = 3$.
- Use the slope to find another point
The slope is $-3$, which can be interpreted as "$\downarrow 3$" for each step to the right. Start from the y-intercept (0, 3):
- Move right 1 unit to $x = 1$, then move down 3 units to $y = 0$. This gives the point (1, 0).
- Plot the second point
Plot the point (1, 0) on the graph.
- Draw the line
Connect the points (0, 3) and (1, 0) with a straight line, extending it in both directions, and add arrows on both ends to indicate it continues indefinitely.
The graph of the line $y = -3x + 3$ is a straight line passing through the points (0, 3) and (1, 0).
More Information
This line has a negative slope, indicating that it descends from left to right. The y-intercept (0, 3) means that the line intersects the y-axis at this point.
Tips
- Forgetting to correctly identify the slope and y-intercept can lead to plotting the line incorrectly.
- Not extending the line in both directions or forgetting to put arrows at the ends.
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