The basis to respond this question are:
1) Perpedicular lines form a 90° angle between them.
2) The product of the slopes of two any perpendicular lines is – 1.
So, from that basic knowledge you can analyze each option:
a.Lines s and t have slopes that are opposite reciprocals.
TRUE. Tha comes the number 2 basic condition for the perpendicular lines.
slope_1 * slope_2 = – 1 => slope_1 = – 1 / slope_2, which is what opposite reciprocals means.
b.Lines s and t have the same slope.
FALSE. We have already stated the the slopes are opposite reciprocals.
c.The product of the slopes of s and t is equal to -1
TRUE: that is one of the basic statements that you need to know and handle.
d.The lines have the same steepness.
FALSE: the slope is a measure of steepness, so they have different steepness.
e.The lines have different y intercepts.
FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.
f.The lines never intersect.
FALSE: perpendicular lines always intersept (in a 90° angle).
g.The intersection of s and t forms right angle.
TRUE: right angle = 90°.
h.If the slope of s is 6, the slope of t is -6
FALSE. – 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is – 1/6.
So, the right choices are a, c and g.