I need some help with MAth?

Question

1. Use the slope-intercept form of a line to determine the relationship between the lines determined by these two equations:3x + 6y = 8
y = 2x- 8

A. parallel
B. perpendicular
C. neither parallel nor perpendicular

2.Use the slope-intercept form of a line to determine the relationship between the lines determined by these two equations:y = x + 5
y = 8- x

A. parallel
B. perpendicular
C. neither parallel nor perpendicular

Answer 1

1) 3x + 6y = 8
y = 2x - 8

First, convert the first equation to slope-intercept form, which is
y = mx + b form.

3x + 6y = 8
6y = -3x + 8
y = (-3/6)x + 8/6
y = (-1/2)x + 8/6

The slope of the first line is 2; the slope of the second line is (-1/2). They are perpendicular, because the product of these slopes is equal to -1.

2) y = x + 5
y = 8 - x

First, convert the second equation to y = mx + b form.

y = 8 - x
y = -x + 8

As you can see, the slope of the first line is 1; the slope of the second line is -1. Their product is -1, so they are perpendicular.

*****
You're going to have three cases:
1) The slopes are the same (in which case, they are parallel
2) The product of the slopes is (-1), in which case, they are perpendicular
3) None of the above. (neither parallel nor perpendicular)

It just happens that these two lines are perpendicular.

Answer 2

OK, slope-intercept form is y = m x + b where m = slope and b = the y intercept

If lines are parallel, they will have the SAME slope (m), if lines are perpendicular, they will have slopes (m) that are negative reciprocals of each other - ex. m = 1/2 (for 1 line)
m = -2 (for the other line)

In your questions:

1. y = 2x-8 m = 2 (slope), b = -8 (y-intercept)
3x + 6y = 8
turn this into slope-intercept form by putting the y on one side
6y = 8 - 3x
now divide by 6 to isolate the y
y = 8/6 - 3x/6
simplify
y = 4/3 - 1/2x
put in slope-intercept form
y = -1/2x + 4/3 m = -1/2 (slope) b = 4/3


Now you see that the 2 slopes are negative reciprocals of each other (2 and -1/2) - this means they are perpendicular lines.



2. y = x + 5 m = 1 (slope) b = 5 (y-intercept)
y = 8 - x
y = -x + 8 (put in slope-intercept form)
m = -1 (slope) b = 8 (y-intercept)
By the slopes, you can tell that these are also perpendicular lines, because -1 is the negative reciprocal of 1.
(1 ---- 1/-1 = -1) << negative reciprocals



Hope this helped.

Answer 3

1) First equation,
3x+6y=8
or, 6y= -3x+8
or, y= -3/6x+8/3
or, y= -1/2x+8/3

2nd equation,
y=2x-8
therefore, the gradient of the two lines are -1/2 & 2, the product of the gradients are -1.
so, the lines are perpendicular to each other.

2) First equation
y=x+5

Second equation
y=8x
or, y= -x+8

therefore, the gradients of the two lines are 1 and-1, and the product of the gradients are -1.

so, the lines are perpendicular

Answer 4

1)y= -1/2x +8/3 (perpendicular)
2) perpendicular