A train track runs parallel to a road represented by the equation \( y = 4x + 17 \). A train station along the track is located at the point \( (6, -1) \). What is the equation of the line that represents the train track?
Answer (2)
The equation of the train track running parallel to the road with equation y = 4x + 17 and passing through the point (6, -1) is y = 4x - 25.
The given equation of the road is y = 4x + 17. If the train track runs parallel to this road, it means that the slope of the train track's line will be the same as the slope of the road. Since the slope of the road is 4 (from the coefficient of x in the equation), the slope of the train track will also be 4. Now, we know a point on the track, which is (6, -1). Using the point-slope form of a line's equation, which is y - y1 = m(x - x1), where (x1, y1) is the point on the line, and m is the slope, we can find the equation of the train track.
Substituting the known values gives us y - (-1) = 4(x - 6), which simplifies to y + 1 = 4x - 24. Subtract 1 from both sides to find the train track's equation: y = 4x - 25.
The equation of the train track, which runs parallel to the road given by y = 4 x + 17 and passes through the point ( 6 , − 1 ) , is y = 4 x − 25 . This was found using the point-slope form of the equation for a line.
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