Final answer:
To convert the equation y = 4x + 9 to standard form, you subtract 4x from both sides to get -4x + y = 9, and then multiply by -1 to obtain 4x - y = -9, which is in the standard form with A, B, and C as integers.
Step-by-step explanation:
To write the equation y = 4x + 9 in standard form using integers, we need to rearrange the equation so that it has the form Ax + By = C, where A, B, and C are integers, and A should be non-negative. Let's perform the transformation step by step:
- Start with the given equation: y = 4x + 9.
- Subtract 4x from both sides of the equation to move the term with the variable x to the left side: -4x + y = 9.
- To ensure that the coefficient for x is non-negative, we can multiply the entire equation by -1 to get: 4x - y = -9, which is now in standard form with A = 4, B = -1, and C = -9.
In the process of constructing a table or plotting points, you would select values for x, calculate the corresponding y values, and then plot these values on a graph to visualize the line as described in Table A1 and Figure A1. Additionally, understanding that equations like 7y = 6x + 8, 4y = 8, and y + 7 = 3x are all linear equations, and understanding the relationship between independent and dependent variables, such as the year and the number of flu cases, is important in the context of mathematics and linear equations.