What is the equation of the line shown, (-4,1) and (2,1)?

Ok, first you need to know the equation of a line: y = mx + b where m is the slope of the line and b is the single point on the line that touches the y axis. 

Let's find m first using the equation for slope. It is the rise of the line which is the difference of the two y coordinates of the points divided by the difference of the two x coordinates of the points (-4,1) and (2,1):

m = (y₂ - y₁)/(x₂ - x₁)

m = (1 - 1)/(-4 - 2)

m = 0/-6

m = 0

This means the lie is going to be completely horizontal since it has no slope.

Now to find b, we have to find the entire equation of the line through a method called "point-slope form" of a line:

y - y₁ = m(x - x₁)

You simply plug a given point into this equation (x₁, y₁) and the slope m, and the equation in the end will look like the standard form y = mx + b:

y - 1 = 0(x - 2)

y -1 = 0

y = 1

This line would go through the y axis at the point (0, 1) and continue onward forever in both directions horizontally.