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.

   Esme's tub already holds water when the circle runs at a steady rate. Points A and B are marked. How many gallons are in the tub at C, at 9 minutes?

   31
2. 2.

   Jun's toy ramp rests on a stack of books. Points A and B are marked on its side view. How high is the ramp at C, 16 inches across?

   14
3. 3.

   Luz's sunflower grows at a steady rate. Points A and B are marked on its height graph. On which day, at C, is it 35 inches tall?

   22
4. 4.

   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
5. 5.

   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
6. 6.

   Tala's sledding hill has slope 0.4. A slope triangle under it has run 6.5 meters. What is its rise, in meters?

   2.6
7. 7.

   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
8. 8.

   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
9. 9.

   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
10. 10.

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

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