Answer: The equation of line r is y = (-10/9)x + 7
Step-by-step explanation:To find the equation of line r, which is parallel to line q, we can use the fact that parallel lines have the same slope.
Line q has an equation of y = -10/9x + 2, where the coefficient of x (-10/9) represents the slope of line q.
Since line r is parallel to line q, it will also have a slope of -10/9.
We are given that line r includes the point (9, -3). To find the equation of line r, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Plugging in the values, we have:
y - (-3) = (-10/9)(x - 9)
Simplifying this equation, we get:
y + 3 = (-10/9)x + 10
To isolate y, we subtract 3 from both sides:
y = (-10/9)x + 7
Therefore, the equation of line r is y = (-10/9)x + 7.