Final answer:
To find the equation of the line passing through the points P(5,-3) and Q(1,1), we can use the point-slope form of a linear equation. The equation of the line is y = -x + 2.
Step-by-step explanation:
To find the equation of the line passing through the points P(5,-3) and Q(1,1), we can use the point-slope form of a linear equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
First, find the slope using the formula: slope = (y2 - y1) / (x2 - x1). Plugging in the values, we get slope = (1 - (-3)) / (1 - 5) = 4 / (-4) = -1.
Now, choose one of the points (P or Q) and substitute the values into the point-slope form: y - (-3) = -1(x - 5). Simplifying the equation gives us y + 3 = -x + 5. Subtracting 3 from both sides gives the final equation: y = -x + 2.