Question

What is the equation in slope-intercept form of the line that passes through the point (2,-5) and is perpendicular to the line represented by y=2x+6

Answer 1

Explanation:

the slope-intercept form is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y- value when x = 0).

the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

a perpendicular slope simply turns the original slope upside-down with x and y, and it flips the sign.

the slope of the origins line is 2 = 2/1.

the perpendicular slope is -1/2.

so, the equation looks like

y = -1/2 x + b

to get b we use the point coordinates :

-5 = -1/2 × 2 + b = -1 + b

-4 = b

so, the full equation is

y = -1/2 x - 4

Answer 2

y = (-1/2)x - 4

Explanation:

y = 2x + 6

Perpendicular: y = (-1/2)x + 6

m = (-1/2); (2, -5)

(x₁, y₁)

y - y₁ = m(x - x₁)

y - (-5) = (-1/2)(x - 2)

y + 5 = (-1/2)x + 1

-5 -5

----------------------------

y = (-1/2)x - 4

I hope this helps!