I can't create visual graphs directly, but I can guide you on how to graph the equation \( y = -\frac{3}{4}x + 5 \).
Steps to Graph the Equation:
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Identify the y-intercept (b):
- In the equation \( y = -\frac{3}{4}x + 5 \), the y-intercept is 5. This means the line crosses the y-axis at the point (0, 5).
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Identify the slope (m):
- The slope is -\(\frac{3}{4}\). This means that for each increase of 1 in the x-direction, the y-value decreases by \(\frac{3}{4}\).
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Plot the y-intercept:
- Start by plotting the point (0, 5) on the graph.
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Use the slope to find another point:
- From (0, 5), move right 4 units (positive x-direction), and then down 3 units (negative y-direction) to get the next point:
- Start at (0, 5): Move right to (4, 5) and then down to (4, 2). Plot the point (4, 2).
- From (0, 5), move right 4 units (positive x-direction), and then down 3 units (negative y-direction) to get the next point:
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Draw the line:
- Draw a straight line through the points (0, 5) and (4, 2).
Additional Point:
To ensure your graph is accurate, you can find another point by plugging in another value for x. For example, if you take \( x = -4 \):
- \( y = -\frac{3}{4}(-4) + 5 = 3 + 5 = 8 \)
- Plot the point (-4, 8).
Final Thoughts:
After plotting at least two points and drawing a line through them, you'll have the graph of the equation \( y = -\frac{3}{4}x + 5 \). The graph will slope downward from left to right due to the negative slope.
You can use graphing software or a graphing calculator if you would like a visual representation right away!