Find the slope of a line with prependicular to each given line

Question

1) x = 3

2) x + 2y = 8

3) y= -1/3 x

Answer 1

1) slope of perpendicular line = 0, x=3 is a vertical line. the perpendicular is a flat horizontal line with zero slope

2) solve the equation for y to get y=-x/2 +4, with slope = -1/2, the coefficient of the x term

perpendicular slope = the negative inverse of the given line's slope of -1/2. flip the fraction upside down and change its sign to get the negative inverse = 2

3) negative inverse of -1/3 = perpendicular slope = 3. when the linear equation is solved for y, the coefficient of the x term is its slope.

it may help to graph the lines, even a rough sketch

for 1) the perpendicular line is y=b where b = any real number. such as y =2

for 2) the perpendicular line is y=2x + b where b =any real number such as 4

for 3) the perpendicular line is y=3x + b where b = any real number such as 0

if you want to graph them