Final answer:
To find the equation of a line parallel to a given line, use the same slope and a different y-intercept.
Step-by-step explanation:
To find the equation of a straight line that is parallel to a given line, we need to know that parallel lines have the same slope. The given line, 6x + 3y = 9, can be rewritten in slope-intercept form as y = -2x + 3. The slope of this line is -2. Since the line we are looking for is parallel, it will also have a slope of -2.
Using the given point (-1,7), we can substitute the values into the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the values, we get y - 7 = -2(x + 1). Simplifying further, we find the equation of the line to be y = -2x + 5.