Write an equation that goes thru (4,2) and is perpendicular to x=-2

Answer 1

X = -2 is vertical line, so we need horizontal line passing point (4,2), this is horizonyal line y = 2

Answer: y = 2

Answer 2

Solution:

The line x =-2 is a vertical line at x = -2 that has an undefined slope because the denominator of the slope equation will be equal to 0, if m is the slope, it will be m = y2-y1/ x2-x1 = y2-y1/ -2-(-2) = y2-y1/0 = ∞ which is undefined. Now any line perpendicular to the vertical line x = -2 is a line that is parallel to the x axis which is also a horizontal line with a slope of m =0.

Using the intercept equation form y = mx+b, and a slope m = 0 then

y = b, where b is the y intercept of the line. With the line passing through the point (4,2), it intersects the y axis at 2, and b = 2. The equation of that line simply becomes y = 2

Also using the slope equation form m = y - 2 / x - 4, with m =0, the equation reduces to y-2 =0 , and y= 2. Both methods leads to the same answer y = 2

Answer 3

It has to be a horizontal line, which is a line of constant y, so the equation is

y = 2