What is the equation of the line that passes through the point 0 , 5 and is parallel to the

Question

What is the equation of the line that passes through the point 0 , 5 and is parallel to the graph of y = 7 x + 4 in the xy -plane?

Accepted Answer

Choice B is correct. The equation of a line in the xy -plane can be written in slope-intercept form y = m x + b , where m is the slope of the line and 0 , b is its y -intercept. It&rsquo;s given that the line passes through the point 0 , 5 . Therefore, b = 5 . It&rsquo;s also given that the line is parallel to the graph of y = 7 x + 4 , which means the line has the same slope as the graph of y = 7 x + 4 . The slope of the graph of y = 7 x + 4 is 7 . Therefore, m = 7 . Substituting 7 for m and 5 for b in the equation y = m x + b yields y = 7 x + 5 . Choice A is incorrect. The graph of this equation passes through the point 0 , 0 , not 0 , 5 , and has a slope of 5 , not 7 . Choice C is incorrect. The graph of this equation passes through the point 0 , 0 , not 0 , 5 . Choice D is incorrect. The graph of this equation passes through the point 0 , 7 , not 0 , 5 , and has a slope of 5 , not 7 .

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