Question

UNIT TEST:

Analytic Geometry - Part 1
(Due 11.2.2023) 4.10 Unit Test: Analytic Geometry - Part 1
Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line-2x + 3y = 12?
Drag each choice into the boxes to correctly complete the table.
Parallel
-2x+y=12
Perpendicular
3x +2y=-2
4
y=z-1 -2x + 3y = 11
1
2
3
4
10
6
7
Ø
Neither
8
9
10
Next

Answer 1

To determine parallel and perpendicular lines, compare their slopes to the given line -2x + 3y = 12.

Step-by-step explanation:

To determine if a line is parallel, perpendicular, or neither to another line, we need to compare their slopes. The given line is -2x + 3y = 12.

To find the slope of this line, we write it in slope-intercept form (y = mx + b) by solving for y: 3y = 2x + 12 ⟹ y = (2/3)x + 4. So, the slope of the given line is 2/3.

Now, let's analyze the other lines:

1. -2x + y = 12: This line has the same slope (2/3) and is parallel to the given line.
2. 3x + 2y = -2: Rearranging this equation in slope-intercept form, we get y = (-3/2)x - 1. The slope of this line is -3/2, which is the negative reciprocal of the given line's slope. Therefore, this line is perpendicular to the given line.
3. y = z - 1: This is not a linear equation and does not represent a line. Therefore, it is neither parallel nor perpendicular to the given line.

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