Identify an equation in point-slope form for the line perpendicular to y = –4x – 1 that passes through (–2, 7).

Slope-intercept form:

y = mx + b       "m" is the slope, "b" is the y-intercept  (it's relevant later)

Point-slope form:

y - y₁ = m(x - x₁)            "m" is the slope

For lines to be perpendicular, their slopes have to be the opposite/negative reciprocal (flipped sign and number)

For example:

slope is 2

perpendicular line's slope is -1/2

slope is -4/5

perpendicular line's slope is 5/4

Since the given line's slope is -4, the perpendicular line's slope is 1/4.

m = 1/4

(x₁ , y₁) = (-2, 7)

Now plug this into the equation:

y - y₁ = m(x - x₁)

y - 7 = 1/4(x - (-2))

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

a: 1/6, j: 1/4

step-by-step explanation: you are welcome