Which graph matches the equation y+3=2(x+3)?

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Sanjeev Kumar 2024-04-19T02:20:18+00:00 1 Answer 14 views
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  1. Pawan Kumar
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    2024-04-19T02:37:27+00:00
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    Here’s a detailed answer to this question on how to determine the graph matching the equation y + 3 = 2(x + 3):

    Understanding the Equation

    • Form: The equation is in point-slope form (y – y₁ = m(x – x₁)), where:
    • m represents the slope
    • (x₁, y₁) is a point that lies on the line.
    • Interpretation:
    • The slope, m, is 2. This tells us the line rises two units for every one unit it moves to the right.
    • The point, (-3, -3), lies on the line.

    Steps to Find the Matching Graph

    1. Rewrite in Slope-Intercept Form:
    • Distribute the 2 in the equation: y + 3 = 2x + 6
    • Isolate y: y = 2x + 3
    1. Identify Key Features:
    • Slope (m) = 2
    • Y-intercept (b) = 3
    1. Examine the Graphs:
    • Look for a graph with a y-intercept of 3 (where the line crosses the y-axis).
    • Check if the line has a positive slope, meaning it goes up as you move from left to right.
    • Verify that the line rises by two units for every one unit it moves to the right (this represents the slope of 2).

    Additional Tips

    • Plot Points: If you’re still unsure, plot the point (-3,-3) from the original equation. From there, use the slope (rise 2, run 1) to find another point on the line. See if the line on the graph passes through these points.
    • Graphing Tools: Consider using online graphing tools or a graphing calculator to plot the equation y = 2x + 3 directly. This helps visualize the line and compare it to the multiple-choice options provided.

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