Let's analyze the equation \( y = 13x - 2 \) and determine which statements are true:
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The graph is a straight line.
- True. Since it's a linear equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, the graph will indeed be a straight line.
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The line passes through the origin.
- False. The line does not pass through the origin because when \( x = 0 \), \( y = -2 \), which means it does not go through the point (0, 0).
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The line passes through the point (0, −2).
- True. When we substitute \( x = 0 \), we get \( y = 13(0) - 2 = -2 \). Therefore, it does pass through the point (0, -2).
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The y-intercept of the line is 2.
- False. The y-intercept \( b \) is -2 (from the equation \( y = 13x - 2 \)), not 2.
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The slope of the line is 3.
- False. The slope \( m \) of the line is 13 (from the equation \( y = 13x - 2 \)), not 3.
Therefore, the true statements about Stella's graph are:
- The graph is a straight line.
- The line passes through the point (0, −2).