Find an equation of the line that passes through the point and has the indicated slope m which is undefined. Point (-3,6)

Answer 1

undefined slope means slope = infinity or negative infinity, or a vertical line

a vertical line means the x coordinate never changes, it's always -3

so the line is x=-3

If you had tried to use the point slope formula

y=mx+b m= infinity, or negative infinity, but there is no y-intercept. the line never crosses the y axis. you can't say b=0 either. As the line doesn't cross at y=0.

b is undefined with no possible value. Solving for b you get a null set. . y is any value, from negative infinity to positive infinity. y is undefined, but can take on any value and does.

You really can't use the point slope formula when m is undefined, y is undefined and b is a null set

Answer 2

An undefined slope means it is a vertical line. Vertical lines have the equation x = some number.

Therefore x must equal -3. then the equation is x = -3.

Answer 3

Equation is y = mx +b

Passing through ( -3,6)

plug in values

6= -m*3 +b

Gives b = 6+3m

So equation is

y = -3m +6+3m

or y = 6

is the equation

So line is parallel to x axis