Question

Use the given conditions to write an equation for the line in the indicated form.

Passing through (2, 2) and perpendicular to the line whose equation is y = 4x + 7;
point-slope form
A)y=-4x-10
B)y-2=-1/4(x-2)
C)y-2=1/4(x+2)
D)y-2=1/4(x-2)

Answer 1

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

Explanation:

Start with the equation of the given line: y = 4x + 7.

Determine the slope of the given line, which is 4.

Since the perpendicular line has a negative reciprocal slope, the perpendicular line's slope is -1/4.

Use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.

Substitute the values x₁ = 2 and y₁ = 2 into the point-slope equation: y - 2 = (-1/4)(x - 2).

Simplify by distributing -1/4 to (x - 2): y - 2 = (-1/4)x + 1/2.

Add 2 to both sides to isolate y: y = (-1/4)x + 1/2 + 2.

Simplify further: y = (-1/4)x + 5/2.

The equation in point-slope form for the line passing through (2, 2) and perpendicular to y = 4x + 7 is y - 2 = (-1/4)(x - 2), which matches option B.