Final answer:
The equation of the line is y - 2 = -4/11(x - 9).
Step-by-step explanation:
To find the equation of the line that passes through the points (9, 2) and (-2, 6), we can use the point-slope form of a linear equation. Point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) are the coordinates of a point on the line, and m is the slope of the line.
First, calculate the slope (m) using the formula: m = (y₂ - y₁) / (x₂ - x₁). Plugging in the coordinates (9, 2) and (-2, 6), we get m = (6 - 2) / (-2 - 9) = -4/11.
Next, choose any point on the line (such as (9, 2)) and plug it into the point-slope form, along with the calculated slope, to obtain the equation of the line. Using (9, 2) as the point and -4/11 as the slope, the equation of the line is y - 2 = -4/11(x - 9).