Given that line s is perpendicular to line t, which statements must be true of the two lines? check all that apply.

a. lines s and t have slopes that are opposite reciprocals.
b. lines s and t have the same slope.
c. the product of the slopes of s and t is equal to -1
d. the lines have the same steepness.
e. the lines have different y intercepts.
f. the lines never intersect.
g. the intersection of s and t forms right angle.
h. if the slope of s is 6, the slope of t is -6

remember, it is check all that apply, so there will be multiple answers.

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.