Write the equation of the line whose slope is undefined and passes through the point (-4,3).

Answer 1

Let's start from the very beginning.

We are able to find the slope of a line by taking two points contained in the line [i.e. (x₁, y₁) and (x₂, y₂)], finding the difference between the two y-values and divide the new value by the difference between the x-values respectively as denoted in the formula below:

m = (y₂ - y₁)/(x₂ - x₁) = Δy/Δx

Note: This is often referred to as rise over run as y-values indicate the vertical position (or rise) while x-values indicate horizontal position (run).

When someone says a line has an undefined slope, what they mean is that the value of the slope is essentially infinite or unattainable. This is achieved when the denominator (bottom portion of a fraction) is equal to zero. You've probably heard it stated that you can't divide by zero. The reason is because the question you're asking when you divide is, "How many times does one value go into another?" Zero goes into all numbers infinite times however, you'll never reach the number regardless of how many zeroes you have. Thus, the slope is undefined.

So we need to take the denominator from the formula above and set it equal to zero to ensure we will achieve an undefined slope.

x₂ - x₁ = Δx = 0

We can plug -4 in for x₁ or x₂. It doesn't matter as long as we keep it in respect to our y-values later.

x₂ - (-4) = 0

x₂ + 4 = 0

Now we solve for x₂.

x₂ = -4

This shows that as long as x is equal to negative four, the line will have an undefined slope.

Therefore, the line we are looking for is:

x = -4

Answer 2

Undefined slopes are for vertical lines crossing the x-axis. Therefore, if the line must pass through point (-4, 3) and have an undefined slope the line would have to be X = -4.

A line with "zero" slope through that same point would be "y = 3" which would go through the y-value of that same point.