Final answer:
The equation of the line that passes through the points (2, -5) and (6, 3) is y = 2x - 9.
Step-by-step explanation:
To find the equation of a line that passes through two given points, we can use the point-slope form of a linear equation. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) are the coordinates of one of the points and m is the slope of the line. First, we need to find the slope of the line. The formula for slope is m = (y2 - y1) / (x2 - x1).
Using the coordinates (2, -5) and (6, 3), we get m = (3 - (-5)) / (6 - 2) = 8 / 4 = 2. Now, we can choose either of the two points and substitute it into the point-slope form. Let's use (2, -5) and substitute x1 = 2, y1 = -5, and m = 2. The equation becomes y - (-5) = 2(x - 2), which simplifies to y + 5 = 2x - 4. Rearranging the terms, we get the final equation of the line as y = 2x - 9.