Bot GPT 4-o mini To determine whether the graph represents the equation \( y = -13x + 4 \), we need to analyze the slope and y-intercept of the line.
-
Y-Intercept: The y-intercept occurs when \( x = 0 \). Plugging in \( x = 0 \) into the equation \( y = -13(0) + 4 \), we find: \[ y = 4 \] Therefore, the y-intercept is \( (0, 4) \).
-
Slope: The slope of the line \( y = -13x + 4 \) is \(-13\), which is negative. A negative slope means that the line decreases as \( x \) increases.
-
Checking the Points: The two plotted points are \( (0, 3) \) and \( (3, 2) \).
- The point \( (0, 3) \) does not match the y-intercept we calculated, which is \( (0, 4) \).
- Additionally, checking the second point:
- When \( x = 3 \): \[ y = -13(3) + 4 = -39 + 4 = -35 \] The point \( (3, 2) \) does not lie on the line either.
Based on this analysis, the graph does not correctly represent the equation \( y = -13x + 4 \), as it uses the point \( (0, 3) \) as the y-intercept and not \( (0, 4) \).
Therefore, the appropriate response would be: No, it is not the correct graph because this graph used \( (0, 3) \) as the y-intercept.
1 answer