Final answer:
To find Alex's weight over time, we use the linear equation y = -2x + 217, where 'y' is the target weight, '-2' is the rate of weight loss per week, and '217' is the starting weight when x = 0.
Step-by-step explanation:
To write a linear equation in slope-intercept form for Alex's weight loss, we need to use the information that he is losing weight at a rate of 2 pounds per week and weighs 205 pounds after 6 weeks. The slope of the equation will be the rate of weight loss (-2 pounds per week), and the y-intercept will be determined by the given weight after 6 weeks.
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
Since Alex is currently 205 pounds after 6 weeks, we can use this to find the y-intercept. We know that over each week, he loses 2 pounds, so after 6 weeks, he would have lost 12 pounds. Assuming he started at 217 pounds (205 pounds + 12 pounds), we can say the y-intercept (b) is 217.
Therefore, the equation representing Alex's weight loss over time will be y = -2x + 217.