To graph the equation \( y = -3x + 5 \), we can identify key points and plot them on a coordinate grid defined by \( x \) and \( y \) values ranging from -10 to 10.
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Identify the y-intercept: The y-intercept occurs when \( x = 0 \). \[ y = -3(0) + 5 = 5 \] So the y-intercept is the point \( (0, 5) \).
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Identify the x-intercept: The x-intercept occurs when \( y = 0 \). \[ 0 = -3x + 5 \implies 3x = 5 \implies x = \frac{5}{3} \approx 1.67 \] So the x-intercept is approximately \( (1.67, 0) \).
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Find another point: Choose another value for \( x \) to find an additional point. Let’s use \( x = 1 \): \[ y = -3(1) + 5 = 2 \] So another point is \( (1, 2) \).
Now, we can plot the points we found:
- Point 1: \( (0, 5) \)
- Point 2: \( (1.67, 0) \)
- Point 3: \( (1, 2) \)
Drawing the Graph
- Draw the x-axis and y-axis.
- Mark the points \( (0, 5) \), \( (1.67, 0) \), and \( (1, 2) \) on the graph.
- Draw a line through these points, extending it in both directions.
Note
Make sure to remember that the slope of -3 indicates that for every one unit increase in \( x \), \( y \) decreases by 3 units, which contributes to the overall downward trend of the line.
This general guideline should help you successfully graph the line represented by the equation \( y = -3x + 5 \) on a grid from -10 to 10.