Explanation:
horizontal line through (2, 5).
that means it is a line of all points with the y-coordinate having the same value. due to the given point that y-coordinate is 5.
therefore, the equation is
y = 5
vertical line through (-9, -3).
that means it is a line of all points with the x-coordinate having the same value. due to the given point that x-coordinate is -9.
therefore, the equation is
x = -9
the slope of a line is the ratio
y coordinate difference / x coordinate difference
when going from one point on the line to another.
for y = 5 the y coordinate difference is always 0 no matter what x-value we use.
the slope is therefore 0/x = 0.
for x = -9 the x coordinate difference is always 0 no matter what y-value we use.
the slope is therefore y/0, and is therefore undefined.