Victory for the ACT Student Text 15e

L ESSON 3 | C OORDINATE G EOMETRY • 229

SLOPE OF A LINE

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ ™Šƒ– ‹• –Š‡ •Ž‘’‡ ‘ˆ the line?

Line l y

is the graph of the equation 2 = + x 2 3 Ǥ Š‡ ‰”ƒ’Š ‘ˆ ™Š‹…Š ‘ˆ –Š‡ ˆ‘ŽŽ‘™‹‰ ‡“—ƒ–‹‘• ‹• ’‡”’‡†‹…—Žƒ” –‘ line l at ( , )0 2 ? A. y x 2 3 2 = − B. y x 3 2 2 = − C. y x 3 2 2 =− + D. y x 2 3 3 =− + E. y x 3 4 = − + {( , ), ( , ), ( , )} 3 4 4 3 2 1 ǡ Š‘™ ƒ› Ž‹‡•…ƒ „‡ †”ƒ™ ™‹–Š ƒ ’‘•‹–‹˜‡ •Ž‘’‡ that include exactly one point from set A and one point from set B ? Ǥ ™‘ G. Three H. Four J. Five K. Six {( , ), ( , ), ( , )} 2 3 1 1 4 5 A set = − − − − B set

7.

9.

Throwback to Math Class A line that runs „‡–™‡‡ , x y 1 1 ^ h and , x y 2 2 ^ h on the coordinate plane Šƒ• –Š‡ ˆ‘ŽŽ‘™‹‰ slope: m x x y y x y 2 1 2 1 T T = − − = If the slope is positive , then as x increases, y increases. If the slope is negative , then as x increases, y decreases. If the slope is 0, then the line is horizontal. If the •Ž‘’‡ ‹• —†‡ϐ‹‡†ǡ then the line is vertical. Use POE In item #7 the ‰”ƒ’Š •Š‘™• –Šƒ– as x increases, y decreases. Use this fact to eliminate ƒ ˆ‡™ ƒ•™‡” choices. Throwback to Math Class ˆ –™‘ Ž‹‡• ƒ”‡ parallel , they have the same slope. ˆ –™‘ Ž‹‡• ƒ”‡ perpendicular , they have negative reciprocal slopes.

A. 3 B. 2 C. 1 D. 1 E. 2

If

, and

10.

 –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ ™Š‹…Š –™‘ •‹†‡• ‘ˆ polygon PQRST have the same slope?

8.

F. PQ G. QR H. PQ J. QR K. RS

and QR and RS and ST and ST and ST