Final answer:
To find the equation of a line parallel to line q, rearrange the equation for line q to the slope-intercept form. The slope of line r will be the same as line q. Finally, use the point-slope form and the coordinates of a point on line r to find its equation.
Step-by-step explanation:
To find the equation of a line parallel to line q, we can use the fact that parallel lines have the same slope. The equation for line q is x - 6y = -6. We can rearrange this equation to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
First, solve the equation for y to get it in the form y = mx + b:
6y = x + 6
y = (1/6)x + 1
Since we know that line r is parallel to line q, it will have the same slope of 1/6. Now we can use the point-slope form of a line to find the equation of line r:
y - y1 = m(x - x1)
Plugging in the coordinates of point (6, -5), we get:
y - (-5) = (1/6)(x - 6)
y + 5 = (1/6)(x - 6)
y = (1/6)x - 1
Therefore, the equation of line r is y = (1/6)x - 1.