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Find the line that is parallel to the line defined by the equation y = 3x + 5 and goes through point (3,2).

User Tomute
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Final answer:

To find a line parallel to y = 3x + 5 and going through the point (3, 2), we use the point-slope form of a line. The equation of the parallel line is y = 3x - 7.

Step-by-step explanation:

To find a line that is parallel to the line y = 3x + 5 and goes through the point (3, 2), we need to find a line with the same slope. The slope of the given line is 3. So, the equation of the new line will also have a slope of 3. Using the point-slope form of a line, y - y1 = m(x - x1), we substitute the values m = 3, x1 = 3, and y1 = 2 to find the equation of the parallel line:

y - 2 = 3(x - 3)

Simplifying the equation:

y - 2 = 3x - 9

y = 3x - 7

Therefore, the line parallel to y = 3x + 5 and passing through the point (3, 2) is y = 3x - 7.

User Monkeyinsight
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