write an equation of the line that is perpendicular to the given line and passes through the given point
A. y=-3x+7 passing through (3, 5)
b. y=8x-1 passing through (4, 10)
A. To find a line that is perpendicular to y = -3x + 7 and passes through (3, 5), we first need to determine the slope of the given line. The slope of the given line is -3.
The slope of a line perpendicular to y = -3x + 7 can be found by taking the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line is 1/3.
Using the point-slope form of a linear equation, where (x₁, y₁) is the given point and m is the slope, we can substitute the values into the equation:
y - y₁ = m(x - x₁)
y - 5 = (1/3)(x - 3)
By distributing the 1/3 on the right side of the equation, we can simplify it:
y - 5 = (1/3)x - 1
Finally, rearranging the equation to slope-intercept form, we get:
y = (1/3)x + 4
Therefore, the equation of the line that is perpendicular to y = -3x + 7 and passes through (3, 5) is y = (1/3)x + 4.
B. To find a line that is perpendicular to y = 8x - 1 and passes through (4, 10), we first need to determine the slope of the given line. The slope of the given line is 8.
The slope of a line perpendicular to y = 8x - 1 can be found by taking the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line is -1/8.
Using the point-slope form of a linear equation, where (x₁, y₁) is the given point and m is the slope, we can substitute the values into the equation:
y - y₁ = m(x - x₁)
y - 10 = (-1/8)(x - 4)
By distributing the -1/8 on the right side of the equation, we can simplify it:
y - 10 = (-1/8)x + 1/2
Finally, rearranging the equation to slope-intercept form, we get:
y = (-1/8)x + 21/2
Therefore, the equation of the line that is perpendicular to y = 8x - 1 and passes through (4, 10) is y = (-1/8)x + 21/2.