Final answer:
To find the equation of a line parallel to a given line and passing through a given point, we need to determine the slope of the given line and substitute the coordinates of the point into the equation.
Step-by-step explanation:
To find an equation of the line that is parallel to 7x + 2y = 5 and passes through the point (0, 6), we need to determine the slope of the given line. The slope of a line parallel to a given line is the same as the slope of the given line. The given line can be rewritten in slope-intercept form as y = -(7/2)x + (5/2). The slope of this line is -7/2.
Since the parallel line has the same slope, the equation of the parallel line can be written as y = -(7/2)x + b, where b is the y-intercept. To find the value of b, we substitute the coordinates of the given point into the equation.
Substituting (0, 6) into the equation, we get 6 = -(7/2)(0) + b. Simplifying, we find that b = 6. Therefore, the equation of the line that passes through (0, 6) and is parallel to 7x + 2y = 5 is y = -(7/2)x + 6.