Why a line has the same slope everywhere (similar triangles)

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Milo's tub already holds some water when the circle runs at a steady rate. Points A and B are marked on the graph. At what time, at point C, does the tub hold 24 gallons?

   11
2. 2.

   Noah starts a hike some miles from home at a steady pace. Points A and B are marked. After how many hours, at C, is Noah 28 miles from home?

   13
3. 3.

   Pia's ramp has slope 1/12. A slope triangle under it has run 18 feet. What is its rise, in feet?

   1 1/2
4. 4.

   Zee's snail graph is a straight line through (0, 0). Its slope triangle has run 3/4 minute and rise 5/6 inch. What rule gives y (inches) for any x (minutes)?

   y = 10x ÷ 9
5. 5.

   Bo's sunflower grows at a steady rate. Its slope triangle has run 3/4 day and rise 4/5 inch. What rule gives y (inches) for any x (days)?

   y = 16x ÷ 15
6. 6.

   The given slope triangle on Esme's roof has run 8 inches and rise 5 inches. A smaller triangle on the roof is half the size of the given one. What is the roof's slope?

   5/8
7. 7.

   Kira's kite string slopes up. A slope triangle has run 6 feet and rise 5 feet. A bigger triangle is 5/2 times as big. What is the slope of the string?

   5/6
8. 8.

   Luz says: "A longer slope triangle on the same ramp has a bigger slope." Which reply is right?

   • Yes: a longer triangle rises more, so its slope is bigger
   • Yes: the slope is bigger near the top of the ramp
   • No: all slope triangles on the ramp are similar, so rise ÷ run is the same
   • No: the slope is the same because the long sides match each other along the ramp
9. 9.

   Milo says: "If I double the run of my slope triangle on the hill, the slope doubles." Which reply is right?

   • Yes: the slope doubles only near the top of the hill
   • No: the slope stays the same because the long sides match
   • No: the rise doubles too, so rise ÷ run stays the same
   • Yes: the run is twice as big, so the slope is twice as big
10. 10.

    Noah says: "A roof line has a steeper slope near the peak than near the edge." Which reply is right?

    • No: slope triangles anywhere on a straight line are similar, so the slope is the same
    • Yes: triangles near the peak are bigger, so their slope is bigger
    • Yes: the line bends upward toward the peak, so the slope grows
    • No: the slope is the same because every triangle has the same rise