Question

1. complete the table.

triangle	vertical side length	horizontal side length	vertical length ÷ horizontal length
cde
fgh

what do you notice? what do you wonder?

1. here are additional lines.

(images of grids with lines labeled a, b, c, d, e, f)
a. match each line shown with a slope from this list: \\(\frac{1}{3}\\), 2, 1, 0.25, \\(\frac{3}{2}\\), \\(\frac{1}{2}\\).
b. one of the given slopes does not have a line to match. draw a line with this slope on the empty grid (f).

Explanation:

Step1: Analyze Line A

Assume each grid square has side length 1. For Line A, the right triangle formed has vertical length (rise) = 3, horizontal length (run) = 2. Slope = $\frac{rise}{run} = \frac{3}{2}$.

Step2: Analyze Line B

For Line B, rise = 1, run = 4. Slope = $\frac{1}{4} = 0.25$.

Step3: Analyze Line C

For Line C, rise = 4, run = 4. Slope = $\frac{4}{4} = 1$.

Step4: Analyze Line D

For Line D, rise = 6, run = 3. Slope = $\frac{6}{3} = 2$.

Step5: Analyze Line E

For Line E, rise = 1, run = 3. Slope = $\frac{1}{3}$.

Step6: Analyze Line F (Empty Grid)

We have slopes: $\frac{1}{3}$, 2, 1, 0.25, $\frac{3}{2}$, $\frac{1}{2}$. Remaining slope is $\frac{1}{2}$. For a line with slope $\frac{1}{2}$, if run = 2, rise = 1 (or run = 4, rise = 2, etc.). Draw a line where for every 2 units right, it goes up 1 unit.

Answer:

A.

• Line A: $\frac{3}{2}$
• Line B: 0.25
• Line C: 1
• Line D: 2
• Line E: $\frac{1}{3}$
• Line F (to draw): $\frac{1}{2}$ (draw a line with rise 1, run 2, e.g., from (0,0) to (2,1) and extend)

B. The slope not matched initially is $\frac{1}{2}$, and the line for it is drawn on grid F with rise 1 and run 2 (or similar proportional rise/run).