write an equation of the line that is perpendicular to the given line and passes through the given point.
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.
In the given equation, y = -8x - 1, the slope is the coefficient of x, which is -8.
Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line perpendicular to y = -8x - 1 would be 1/8.
Now that we have the slope and a point (4, 10), we can use the point-slope form of a linear equation to write the equation of the perpendicular line.
The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Plugging in the values, we get:
y - 10 = 1/8(x - 4)
To simplify, distribute 1/8 to x - 4:
y - 10 = 1/8x - 1/2
Add 10 to both sides to isolate y:
y = 1/8x - 1/2 + 10
Combine the fractions and whole numbers:
y = 1/8x + 19/2
Therefore, the equation of the line that is perpendicular to y = -8x - 1 and passes through (4, 10) is y = 1/8x + 19/2.