m= undefined, crossing through (-3,5)

Question

The directions of this problem is "Write an equation in slope intercept form for the line that satisfies the given conditions"

Answer 1

The equation of a line in slope-intercept form looks like the following:   y = mx + b , 

where m is the slope of the line and b is the y-intercept.

Given any 2 points (x₁, y₁) and (x₂, y₂) on a line, the slope (m) = (y₂-y₁)/(x₂-x₁).

Whenever the slope (m) is undefined it means that when you try to calculate the slope given any 2 points on the line you'll end up with a zero in the denominator, which is undefined. That is, with an undefined slope you end up with a vertical line, which has the equation "x=some number".

That is, m = (y₂-y₁)/(x₂-x₁) = (y₂-y₁)/0 = undefined. This implies that x₂=x₁. So x is the same for any value of y on the line, which is why the equation is "x=some number" and the line is vertical. 

So the equation of a line, in slope-intercept form, with an undefined slope (m=undefined) crossing through the point (-3, 5) is:   x= -3 , which is a vertical line.