suppose we are given the following.\nline 1 passes through (0, 2) and (-3, 8).\nline 2 passes through (-3…

suppose we are given the following.\nline 1 passes through (0, 2) and (-3, 8).\nline 2 passes through (-3, 3) and (1, -5).\nline 3 passes through (-3, 0) and (1, 8).\n(a) find the slope of each line.\nslope of line 1: \nslope of line 2: \nslope of line 3: \n(b) for each pair of lines, determine whether they are parallel, perpendicular, or neither.\nline 1 and line 2: parallel perpendicular neither\nline 1 and line 3: parallel perpendicular neither\nline 2 and line 3: parallel perpendicular neither

suppose we are given the following.\nline 1 passes through (0, 2) and (-3, 8).\nline 2 passes through (-3, 3) and (1, -5).\nline 3 passes through (-3, 0) and (1, 8).\n(a) find the slope of each line.\nslope of line 1: \nslope of line 2: \nslope of line 3: \n(b) for each pair of lines, determine whether they are parallel, perpendicular, or neither.\nline 1 and line 2: parallel perpendicular neither\nline 1 and line 3: parallel perpendicular neither\nline 2 and line 3: parallel perpendicular neither

Answer

Explanation:

Step1: Calculate slope of Line 1

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). For Line 1 with ((x_1,y_1)=(0,2)) and ((x_2,y_2)=(-3,8)), we have (m_1=\frac{8 - 2}{-3-0}=\frac{6}{-3}=-2).

Step2: Calculate slope of Line 2

For Line 2 with ((x_1,y_1)=(-3,3)) and ((x_2,y_2)=(1,-5)), (m_2=\frac{-5 - 3}{1-(-3)}=\frac{-8}{4}=-2).

Step3: Calculate slope of Line 3

For Line 3 with ((x_1,y_1)=(-3,0)) and ((x_2,y_2)=(1,8)), (m_3=\frac{8 - 0}{1-(-3)}=\frac{8}{4}=2).

Step4: Determine relationship between Line 1 and Line 2

Since (m_1=-2) and (m_2=-2), (m_1 = m_2). So Line 1 and Line 2 are parallel.

Step5: Determine relationship between Line 1 and Line 3

Since (m_1=-2) and (m_3 = 2), (m_1\times m_3=-4\neq - 1) (for perpendicular (m_1\times m_2=-1)) and (m_1\neq m_3). So Line 1 and Line 3 are neither.

Step6: Determine relationship between Line 2 and Line 3

Since (m_2=-2) and (m_3 = 2), (m_2\times m_3=-4\neq - 1) and (m_2\neq m_3). So Line 2 and Line 3 are neither.

Answer:

(a) Slope of Line 1: (-2); Slope of Line 2: (-2); Slope of Line 3: (2) (b) Line 1 and Line 2: Parallel; Line 1 and Line 3: Neither; Line 2 and Line 3: Neither