Answer:
Explanation:
The equation of line p is given as y = ax + b. We need to determine which equation could represent line q.
Let's analyze each option:
Option 1: y = -3a(x+6) + b
In this equation, the x-term is multiplied by -3a and there is a positive constant 6 added inside the parentheses. The constant term b remains the same. This equation represents a line with a negative slope of -3a and a y-intercept of b.
Option 2: y = 3a(x+6) + b
This equation is similar to the previous one, but the x-term is multiplied by 3a instead of -3a. Therefore, the slope of the line is positive (3a) and the y-intercept is b.
Option 3: y = -3ax + b + 6
In this equation, the x-term is multiplied by -3a, and there is a constant term 6 added outside the parentheses. The constant term b remains the same. This equation represents a line with a negative slope of -3a and a positive constant shift of 6 on the y-axis.
Option 4: y = 3ax + b - 6
Similar to the previous equation, the x-term is multiplied by 3a, and there is a constant term -6 subtracted outside the parentheses. The constant term b remains the same. This equation represents a line with a positive slope of 3a and a negative constant shift of 6 on the y-axis.
Based on the analysis, options 1, 2, 3, and 4 could all be equations of line q. The difference lies in the slope and any constant shifts on the y-axis. The specific values of a, b, and the constant terms determine the exact characteristics of line q.
I hope this helps! Let me know if you have any further questions.