Identify an equation in point-slope form for the line perpendicular to y = -4x - 1 that passes through (-2,7)
To find the equation of the line perpendicular to y = -4x - 1, we need to first find the slope of the given line. The slope of y = -4x - 1 is -4.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. So, the slope of the perpendicular line is 1/4.
Now, we can use the point-slope form of the equation of a line to find the equation of the line passing through the point (-2,7) with a slope of 1/4:
y - y1 = m(x - x1)
Where y1 = 7, x1 = -2, and m = 1/4:
y - 7 = 1/4(x - (-2))
y - 7 = 1/4(x + 2)
y - 7 = 1/4x + 1/2
Therefore, the equation in point-slope form for the line perpendicular to y = -4x - 1 that passes through (-2,7) is y - 7 = 1/4x + 1/2.