Write an equation of the line containing the given point and parallel to the given line. (6, -6); 7x-2y=5

2 y = 7 x - 5

y = (7/2) x -5/2
so slope of parallel line is also (7/2)

y = (7/2) x + b
-6 = (7/2)(6) + b
-6 = 21 + b
b = -27
so

y = (7/2) x - 27

To find the equation of a line that is parallel to a given line, we need to have the same slope.

The given line is represented by the equation 7x - 2y = 5. We can rewrite this equation in slope-intercept form (y = mx + b), where "m" represents the slope:

7x - 2y = 5
-2y = -7x + 5
y = (7/2)x - 5/2

From the given equation, we observe that the slope of the line is 7/2.

Since the line we want to find is parallel to the given line, it will also have a slope of 7/2.

Now that we have the slope and a point (6, -6) on the line, we can use the point-slope form (y - y₁ = m(x - x₁)) to find the equation of the line:

y - (-6) = (7/2)(x - 6)
y + 6 = (7/2)x - 21
y = (7/2)x - 27

Therefore, the equation of the line containing the point (6, -6) and parallel to the given line 7x - 2y = 5 is y = (7/2)x - 27.