write an equation of the line that is perpendicular to the given line the passes through the given point .
B. y = 8x - 1 passing through (4, 10)
To find the equation of the 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 given line has a slope of 8, so the perpendicular line will have a slope that is the negative reciprocal of 8.
The negative reciprocal of 8 is -1/8, so the slope of the perpendicular line is -1/8.
Next, we can use the point-slope form of a line to find the equation of the line.
The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Using the point (4, 10) and the slope -1/8, we have:
y - 10 = (-1/8)(x - 4)
Simplifying the equation:
y - 10 = (-1/8)x + 1/2
The equation in slope-intercept form is:
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.