Standard form equation of the line perpendicular to y = 2x -3 through (1,5)
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.
To find the equation of the line perpendicular to the given line, we need to determine the slope of the given line, and then find the negative reciprocal to get the slope of the perpendicular line.
The given line is in the form y = mx + b, where m represents the slope. In this case, the slope is 2.
The negative reciprocal of 2 is -1/2. This will be the slope of the perpendicular line.
Now that we have the slope, we can use the point-slope form of the equation of a line, which is y - y₁ = m(x - x₁), where (x₁, y₁) represents the coordinates of a point on the line.
Substituting the values (1, 5) for (x₁, y₁) and -1/2 for m, we get:
y - 5 = -1/2(x - 1)
To convert this equation to standard form, we multiply everything by 2 to eliminate the fraction:
2y - 10 = -x + 1
Rearranging the terms, we get:
x + 2y = 11
Therefore, the standard form equation of the line perpendicular to y = 2x - 3 and passing through the point (1,5) is x + 2y = 11.
To find the standard form equation of a line perpendicular to a given line, you need to consider the slope of the given line.
Given that the equation of the given line is y = 2x - 3, we can determine its slope by looking at the coefficient of x. In this case, the slope of the given line is 2.
The slope of any line perpendicular to this line can be found by taking the negative reciprocal of the given line's slope. The negative reciprocal of 2 is -1/2.
Now that we have the slope of the perpendicular line, we can use the point-slope form of a line to find its equation. The point-slope form is given as: y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line, and m is the slope of the line.
Using the point (1, 5) and the slope -1/2, we can substitute these values into the point-slope form equation:
y - 5 = (-1/2)(x - 1)
Next, we can simplify the equation by distributing -1/2 to the terms in parentheses:
y - 5 = (-1/2)x + 1/2
To eliminate the fractions, we can multiply the entire equation by 2:
2(y - 5) = -x + 1
Expanding the left side, we get:
2y - 10 = -x + 1
To put the equation in standard form, we move all the terms to the left side and arrange them in the form Ax + By = C:
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.