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What is the geometric representation of the equation 3x - 4y = 12?
What is the geometric representation of the equation 3x - 4y = 12?
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What is the geometric representation of the equation 3x - 4y = 12?
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Linear equations represent straight lines in a two-dimensional space.
Questions & Step-by-step Solutions
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Q: What is the geometric representation of the equation 3x - 4y = 12?
Solution:
Linear equations represent straight lines in a two-dimensional space.
Steps: 8
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Step 1: Understand that the equation 3x - 4y = 12 is a linear equation.
Step 2: Rearrange the equation into the slope-intercept form (y = mx + b).
Step 3: Solve for y: Start with 3x - 4y = 12, then subtract 3x from both sides to get -4y = -3x + 12.
Step 4: Divide every term by -4 to isolate y: y = (3/4)x - 3.
Step 5: Identify the slope (m) and y-intercept (b) from the equation y = (3/4)x - 3. Here, m = 3/4 and b = -3.
Step 6: Plot the y-intercept (0, -3) on a graph.
Step 7: Use the slope (3/4) to find another point: from (0, -3), go up 3 units and right 4 units to (4, 0).
Step 8: Draw a straight line through the points (0, -3) and (4, 0). This line represents the equation 3x - 4y = 12.
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