Write the equation of a line that goes through the point ( 6 ,6 ) and is parallel to the line y = 1 / 3x - 4.
Question
Write the equation of a line that goes through the point ( 6 ,6 ) and is parallel to the line
Solution
Step 1: Identify the slope of the given line The equation of the given line is in the form y = mx + c, where m is the slope. Here, m = 1/3.
Step 2: Use the slope of the parallel line Parallel lines have the same slope. So, the slope of the line we want to find is also 1/3.
Step 3: Use the point-slope form of a line The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We know that our line passes through the point (6, 6) and has a slope of 1/3. Substituting these values in, we get:
y - 6 = 1/3(x - 6)
Step 4: Simplify the equation To simplify, distribute the 1/3 on the right side:
y - 6 = 1/3x - 2
Then, add 6 to both sides to solve for y:
y = 1/3x + 4
So, the equation of the line that goes through the point (6, 6) and is parallel to the line y = 1/3x - 4 is y = 1/3x + 4.
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