Question

Determine which of the lines, if any, are parallel or perpendicular. Explain. Line a:2x+6y=-12, Line b:y=(3)/(2)x-5, Line c:3x-2y=-4

Answer 1

To determine if lines are parallel or perpendicular, we can look at their slopes.

Step-by-step explanation:

Line a: 2x+6y=-12. To determine if lines are parallel or perpendicular, we can look at their slopes. The slope of a line can be found by rearranging the equation into slope-intercept form y=mx+b, where m is the slope. For line a, we need to rearrange the equation to slope-intercept form:

2x+6y=-12

6y=-2x-12

y=(-2)/(6)x-2

The slope of line a is -2/6 or -1/3. Now let's find the slopes of lines b and c:

Line b: y=(3)/(2)x-5. The slope of line b is 3/2 which is different from the slope of line a. Therefore, line a and line b are not parallel or perpendicular.

Line c: 3x-2y=-4. Rearranging the equation to slope-intercept form:

3x-2y=-4

-2y=-3x-4

y=(3)/(2)x+2

The slope of line c is 3/2 which is the same as the slope of line b. Therefore, line b and line c are parallel. Line c is not perpendicular to line a or b.

Answer 2

To determine parallel or perpendicular lines, we compare their slopes. Line b and line c are parallel, while line a is perpendicular to lines b and c.

Step-by-step explanation:

To determine which lines, if any, are parallel or perpendicular, we can compare the slopes of the lines. In slope-intercept form (y = mx + b), the slope of a line is represented by the coefficient of x. If two lines have the same slope, they are parallel. If the slopes of two lines are negative reciprocals of each other, they are perpendicular.

Line a: 2x + 6y = -12 in slope-intercept form is y = -1/3x - 2. Therefore, the slope of line a is -1/3.

Line b: y = (3/2)x - 5. The slope of line b is 3/2.

Line c: 3x - 2y = -4 in slope-intercept form is y = (3/2)x + 2. Therefore, the slope of line c is 3/2.

Comparing the slopes, we can see that the slopes of line b and line c are the same, so they are parallel to each other. Line a has a slope that is the negative reciprocal of the slopes of lines b and c, so it is perpendicular to them.