The equation for the horizontal line that contains the point e(3, –4)?

The slope of a  horizontal line will have a value equal to 0: 
m=0
Point-slope form of a line: we need a point (x₀,y₀) and the slope "m".
y-y₀=m(x-x₀)

We have a point ( E(3,-4) ) and the slope of this line (m=0); therefore:y
y+4=0(x-3=
y+4=0
y=-4

the equation for the horizontal line that contains the point E, would be:
y=-4

Where m is the slope of the line and b is the y-intercept of the line, or the y-coordinate of the point at which the line crosses the y-axis. to write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. this is the value of m in the equation.