Final answer:
To convert an equation from slope-intercept form (y = mx + b) to standard form (Ax + By = C), subtract mx from both sides and then ensure all coefficients are integers, arranging to have the x term's coefficient be positive.
Step-by-step explanation:
Converting an equation from slope-intercept form to standard form involves rearranging the equation so that all terms are on one side and the x and y variables are both on the same side. The slope-intercept form of a linear equation is usually written as y = mx + b, where m represents the slope and b represents the y-intercept.
To convert it to standard form, which is Ax + By = C, where A, B, and C are integers, you need to move the x-term to the same side as the y-term by subtracting mx from both sides and then simplify the coefficients to be integers, if necessary.
For example, consider the slope-intercept equation y = 3x + 9. To convert this to standard form, you would subtract 3x from both sides to get -3x + y = 9. You may need to multiply through by -1 to ensure that the coefficient of x is positive, which gives the standard form 3x - y = -9.