what is an equation of the line that passes through the point (7,-7) abd is perpendicular to the line x-2y=2

Answer 1

After solving for y in the equation and getting y = (1/2)x - 1, we can see that the slope is 1/2 so the negative reciprocal -2 is the slope of the perpendicular line. When deriving the equation for the perpendicular line, we can plug the point (7, -7) into the slope intercept form y₂ - y₁ = m(x₂ - x₁) as follows:

y₂ - y₁ = m(x₂ - x₁)

y + 7 = -2(x - 7)

y = -2x + 7

Answer 2

Hello, Cruz,

Let's put x-2y=2 into slope intercept format:

-2y = -x+2

y = (1/2)x - 1

The slope, m, is (1/2).

A line perpendicular to any line in this format will have a slope that is the negative inverse of the line's slope. In this case, the perpendicular line slope becomes -2 (negative inverse).

The new line is taking shape:

y = 2x + b

We need to find b, the y intercept ( the value of y when x = 0). To find b, use the point given (7,-7). It is a point on the perpendicular line, so we can insert the values of x and y, and then solve for b.

-7 = 2*(7) + b

b = -7 - 14

b = - 21

The perpendicular line becomes y = 2x - 21

Bob