Question

if placed on a coordinate grid, each of the triangles in set 1 could lie on the same graphed line as a triangle in set 2. using the typing tool fill in each white box to complete the sentences at the bottom
set 1
set 2
triangles a and could lie on a graphed line with a slope of
triangles b and could lie on a graphed line with a slope of
triangles c and could lie on a graphed line with a slope of

Explanation:

Step1: Recall slope formula

The slope of a right - triangle (used as a slope - triangle) is given by $\frac{\text{rise}}{\text{run}}$.

Step2: Calculate slope for Triangle A

For Triangle A, if we assume the vertical side (rise) is 54 and the horizontal side (run) is 9, then the slope $m_A=\frac{54}{9} = 6$.

Step3: Find a triangle in Set 2 with slope 6

For Triangle D in Set 2, with rise 16 and run $\frac{16}{6}=\frac{8}{3}
eq6$. For Triangle E, with rise $\frac{7}{2}$ and run 12, $m_E=\frac{\frac{7}{2}}{12}=\frac{7}{24}
eq6$. For Triangle F, if we assume the vertical side is 13 and the horizontal side is 52, then $m_F=\frac{13}{52}=\frac{1}{4}
eq6$.

Step4: Calculate slope for Triangle B

For Triangle B, if the rise is 60 and the run is 15, then the slope $m_B=\frac{60}{15}=4$.

Step5: Find a triangle in Set 2 with slope 4

For Triangle D, $m_D=\frac{16}{4} = 4$.

Step6: Calculate slope for Triangle C

For Triangle C, if the rise is 18 and the run is 45, then the slope $m_C=\frac{18}{45}=\frac{2}{5}$.

Step7: Find a triangle in Set 2 with slope $\frac{2}{5}$

For Triangle E, if we consider the rise $\frac{7}{2}$ and run 12, $m_E
eq\frac{2}{5}$. For Triangle F, $m_F
eq\frac{2}{5}$. For Triangle D, $m_D
eq\frac{2}{5}$.

Answer:

Triangles A and none could lie on a graphed line with a slope of 6.
Triangles B and D could lie on a graphed line with a slope of 4.
Triangles C and none could lie on a graphed line with a slope of $\frac{2}{5}$.