Final answer:
To write the equation in slope-intercept form, we need to find the slope and the y-intercept. Using the given points P(5,5) and Q(-1,-1), the slope is 1 and the y-intercept is 0. Therefore, the equation of the line is y = x.
Step-by-step explanation:
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b). The slope can be calculated using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the values from the given points, P(5,5) and Q(-1,-1), we get: m = (-1 - 5) / (-1 - 5) = (-6) / (-6) = 1. The y-intercept can be found by substituting the slope and one of the points into the slope-intercept form and solving for b. Using point P(5,5), we have: 5 = (1)(5) + b, which simplifies to: 5 = 5 + b. Subtracting 5 from both sides, we get: b = 0. Therefore, the equation in slope-intercept form is: y = 1x + 0, which simplifies to: y = x.