Final answer:The slope of a line parallel to the line 4x - 7y = -14 is determined by converting the equation to slope-intercept form, revealing that the slope is 4/7. Thus, any line parallel to it will have the same slope of 4/7.Explanation:The slope of a line parallel to the line4x - 7y = -14is first determined by rewriting the given line in slope-intercept form (y = mx + b), wheremrepresents the slope. For the line 4x - 7y = -14, we can solve foryto find the slope:Add 7y to both sides: 4x = 7y - 14.Then add 14 to both sides: 4x + 14 = 7y.Finally, divide every term by 7 to solve fory: (4/7)x + 2 = y.The slope of the line is4/7. Since parallel lines have equal slopes, any line parallel to the given line will also have a slope of4/7....

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