Questions: Which of the following graphs represents the equation y=3x+2? A. Graph A B. Graph B C. Graph C D. Graph D

Which of the following graphs represents the equation y=3x+2? A. Graph A B. Graph B C. Graph C D. Graph D
Transcript text: Which of the following graphs represents the equation $y=3 x+2$ ? A. Graph A B. Graph B C. Graph C D. Graph D
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Solution

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Solution Steps

Step 1: Identify the equation's slope and y-intercept

The given equation is \( y = 3x + 2 \). Here, the slope (m) is 3, and the y-intercept (b) is 2.

Step 2: Check the y-intercept in each graph
  • Graph A: y-intercept is 1
  • Graph B: y-intercept is 2
  • Graph C: y-intercept is 2
  • Graph D: y-intercept is -2

Graphs B and C have the correct y-intercept of 2.

Step 3: Verify the slope in the remaining graphs
  • For Graph B: Check the points (0, 2) and (2, 6). The slope is \((6-2)/(2-0) = 4/2 = 2\).
  • For Graph C: Check the points (0, 2) and (-1, -1). The slope is \((2 - (-1))/(0 - (-1)) = 3/1 = 3\).

Graph C has the correct slope of 3.

Final Answer

Graph C

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