Find the equation of a line through (2, 5) which is perpendicular to the line y = 4x + 1, and put it in the form y = mx + b
you want the slope to be -1/4, so the point-slope form is
y-5 = -1/4 (x-1)
now rearrange that to slope-intercept form.
Thanks so much
To find the equation of a line perpendicular to another line, we need to follow a few steps.
Step 1: Find the slope of the given line.
The given line is y = 4x + 1, where the coefficient of x is the slope. So, the slope of the line is 4.
Step 2: Find the negative reciprocal of the slope.
Perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of 4 is -1/4.
Step 3: Use the slope and the given point to determine the equation.
We have the point (2, 5) and the slope -1/4. We can use the point-slope form of a linear equation:
(y - y1) = m(x - x1)
Replacing y1 with 5, x1 with 2, and m with -1/4, we get:
(y - 5) = -1/4(x - 2)
Step 4: Simplify the equation.
Distributing -1/4 to (x - 2), we get:
(y - 5) = (-1/4)x + 1/2
Rearranging the equation by isolating y, we get:
y = (-1/4)x + 1/2 + 5
Combining like terms, we get:
y = (-1/4)x + 11/2
So, the equation of the line through (2, 5) perpendicular to y = 4x + 1 is y = (-1/4)x + 11/2 in the form y = mx + b.