Tip #12 to Get a Top SAT Math Score

Here are the rest of the slope rules on the SAT. You should memorize these; they are on every SAT!

• Parallel lines have equal slopes.
• Perpendicular lines have negative reciprocal slopes,

Example: .

• Lines reflected over the x axis or y axis have negative slopes

Example: .

A reflection is like a mirror image. In the diagram to the right, line m is the reflection of line l over the x axis

• Skill 30 preview: A line expressed in the form y = ax + b has a slope of a. If the line is given in standard form Ax + By = C, use algebra to convert it to y = ax + b form.

Let's look at this question:

Solution: This question is quite difficult for most students. But with our strategies it's very easy. We know that two lines that are reflections of each other simply have the same slope but with opposite signs; so instead of –, line j has a slope of +.

Correct answer: B

Example Problems

Medium

1. What is the slope of the line perpendicular to the line through the points (2, 3) and (–1, 0) ?
   1. A –1
   2. B 0
   3. C 1
   4. D 3
   5. E Undefined
2. If the line through the points (2, –3) and (4, p) is parallel to the line y = –2x – 3 what is the value of p ?
   1. A 7
   2. B 3
   3. C 0
   4. D –3
   5. E –7
3. What is the slope of the line perpendicular to the line through the point (2, –3) and the origin?
   1. A 0.4
   2. B
   3. C 1
   4. D –2
   5. E 0.5
4. In the xy coordinate plane, line n is the reflection of line m about the x axis. If the slope of line m is , what is the slope of line n ?
   1. A 1
   2. B –1
   3. C
   4. D –
   5. E–

Hard

5. If the slope of a line through the points (2, 4) and (0, b) is 1, and the line through (b, 4) and (m, 6) is parallel to that line, what is the value of m ?
   1. A 0
   2. B 2
   3. C 4
   4. D 6
   5. E 8