# Write the point-slope form of an equation for the horizontal line that passes through (-4, -1).

ncchemist | Certified Educator

The point slope form of a linear equation is written below:

y-y1 = m(x-x1)

m is the slope of the equation and x1 and y1 are the coordinates for a point on the equation.  So if we have a slope and the coordinates for a point then we can plug them into the above equation to get the point slope form of the line.  So if we are looking at the equation for a horizontal line that passes through (-4,-1), we are already given a point to plug into the equation.  Slope is rise over run, and a horizontal line has no rise (it has a constant value of y for any x) so its slope is 0.  We can now plug these values into the equation:

y-(-1) = 0(x-(-4))

y+1 = 0(x+4)

y+1 = 0

violy | Certified Educator

Taking note that slope of a horizontal line is zero, we can use the slope-intercept form y = mx + b; where m = slope, x = abscissa, and y = ordinate.

Plugging-in y = -1, m = 0 and x = -4 on y = mx + b:

- 1 = 0(-4) + b

- 1 = 0 + b

- 1 = b     or  b = -1.

Plugging-in m = 0 and b = -1 on y = mx + b:

y = 0x - 1

==> y = -1 or y + 1 = 0.