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,
- Lines reflected over the x axis or y axis have negative slopes
- 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.
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
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
- What is the slope of the line perpendicular to the line through the points (2, 3) and (–1, 0) ?
- A –1
- B 0
- C 1
- D 3
- E Undefined
- 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 ?
- A 7
- B 3
- C 0
- D –3
- E –7
- What is the slope of the line perpendicular to the line through the point (2, –3) and the origin?
- A 0.4
- C 1
- D –2
- E 0.5
- 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 ?
- A 1
- B –1
- D –
- 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 ?
- A 0
- B 2
- C 4
- D 6
- E 8
- A Plug the two points into the slope equation. = 1 Since we want the line to be perpendicular, take the negative reciprocal, –1.
- E Parallel lines have equal slopes. The slope of line y = –2x – 3 is –2 (which we will review in Skill 30), so the slope of the two points given is = –2 "Use the Answers" or cross–multiply (see Skill 20) to solve for p. p= –7.
- B The origin means (0, 0). Plug the two points into the slope equation.
- D 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 have slopes with opposite signs, so instead of 2/3, line n has a slope of –2/3.
- C Use the slope formula to solve for b. Then use the value of b in the slope formula for the second pair of points, and solve for m. Because the lines are parallel, the second pair also has a slope equal to 1.
Since we want the slope of a line perpendicular, we take the negative reciprocal, which is
Go to: Tip #13