Question

What is the point-slope form of the equation for the line with a slope of -2 that passes through the point (4, -6)?

a) y- 4 = -2(2+6)
b) y=-2.1 - 6
c) y-6= -2(2+4)
d) y+6= -2(2 - 4)

Answer 1

y + 6 = -2(x-4)

None of the answer options match this equation. Is option d) y + 6 = -2(2-4) mistyped? Was the 2 in the parentheses (2-4) meant to be x (x-4)?

Step-by-step explanation:

Point slope form is given by:

y-y₁=m(x-x₁)

Use the one given point,

(4,-6) as (x₁, y₁)

y-(-6)=m(x-4)

y + 6 = m(x-4)

slope, m, is -2:

y + 6 = -2(x-4)

This does not match any of the answer options. d) y+6= -2(2 - 4) comes close, with the exception of the 2 in the parentheses. As written, it reduces to:

d) y+6= -2(2 - 4)

y+6= -2(-2)

y = -2 This is a horizontal line. x does not appear in the equation.

If if were written with an x, it would match: d) y+6= -2(x - 4)

Answer 2

The correct point-slope form for the line with a slope of -2 that passes through (4, -6) is y + 6 = -2(x - 4).

Step-by-step explanation:

The point-slope form of the equation for a line with a slope of -2 that passes through the point (4, -6) is given by the formula y - y1 = m(x - x1), where (x1, y1) is the point it passes through and m is the slope.

In this case, the equation would be y - (-6) = -2(x - 4). Simplifying this, we get y + 6 = -2(x - 4), which matches option d) y+6= -2(x - 4).