Line L is perpendicular to the line y x3 2 5+ = and passes through P.Find the equation of line L.
Question
Line L is perpendicular to the line y x3 2 5+ = and passes through P.Find the equation of line L.
Solution
The equation of the line given is y = 2x + 3.
Step 1: Find the slope of the given line The slope of the line y = 2x + 3 is 2.
Step 2: Find the slope of the perpendicular line The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. So, the slope of the line L is -1/2.
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 line L passes through the point P, but we don't know the coordinates of P. Let's assume that P has coordinates (a, b).
Step 4: Substitute the values into the point-slope form Substituting the values into the point-slope form, we get y - b = -1/2(x - a).
Step 5: Rearrange the equation Rearranging the equation to the slope-intercept form (y = mx + c), we get y = -1/2x + (b + a/2).
So, the equation of line L is y = -1/2x + (b + a/2). We can't simplify it further without knowing the coordinates of the point P.
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