Question
Standard form equation of the line perpendicular to y = 2x -3 through (1,5)
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GPT 3.5
To find the standard form equation of a line perpendicular to y = 2x - 3, we need to determine the slope of the perpendicular line.
The slope of the given line y = 2x - 3 is 2.
The slope of a line perpendicular to y = 2x - 3 will have a slope that is the negative reciprocal of 2, so the slope of the perpendicular line will be -1/2.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can substitute in the given point (1,5) and the slope -1/2 to find the equation of the perpendicular line:
y - 5 = -1/2(x - 1)
Multiplying both sides of the equation by 2 to eliminate the fraction:
2(y - 5) = -1(x - 1)
Expanding the equation:
2y - 10 = -x + 1
Rearranging the equation to be in standard form Ax + By = C format:
x + 2y = 11
Therefore, the standard form equation of the line perpendicular to y = 2x - 3 through the point (1,5) is x + 2y = 11.
The slope of the given line y = 2x - 3 is 2.
The slope of a line perpendicular to y = 2x - 3 will have a slope that is the negative reciprocal of 2, so the slope of the perpendicular line will be -1/2.
Using the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can substitute in the given point (1,5) and the slope -1/2 to find the equation of the perpendicular line:
y - 5 = -1/2(x - 1)
Multiplying both sides of the equation by 2 to eliminate the fraction:
2(y - 5) = -1(x - 1)
Expanding the equation:
2y - 10 = -x + 1
Rearranging the equation to be in standard form Ax + By = C format:
x + 2y = 11
Therefore, the standard form equation of the line perpendicular to y = 2x - 3 through the point (1,5) is x + 2y = 11.