Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points.
(-1, -4) and (0,0)
(a) select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a) The slope of the line is parallel to the another line m=4

b) The slope of the line is perpendicular to the another line m=

Step-by-step explanation:

Step1:-

Slope of a line :-

If θ is the inclination of a line 'l' then tanθ is called the slope or gradient of the line 'l'.The slope of a line is denoted by m=tanθ

The slope of a line given two points m=

Parallel lines:-

Two non-vertical lines are parallel if and only if their slopes are parallel

Perpendicular lines:-

Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

Step 2:-

a)The slope of a line when given two points (-1,-4) and (0,0)

Two non-vertical lines are parallel if and only if their slopes are parallel

Therefore the slope of the line that is parallel to the another line

Step 3:-

b) Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

Therefore the slope of the line is perpendicular to the another line is

a) 4

b) - 1/4

Step-by-step explanation:

The given line passes through the pair of points, (-1, -4) and (0,0)

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

Looking at the pair of points,

y2 = 0

y1 = - 4

x2 = 0

x1 = - 1

Slope = (0 - - 4)/(0 - - 1) = 4/1 = 4

a) if two lines are parallel, it means that they have the same slope. This means that the slope of the line that is parallel to the given line is 4

b) if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the other line. This means that the slope of the line that is perpendicular to the given line is - 1/4

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

the camry sales+accord sale=828,000. to make it so the two numbers are 18 thousand apart and still equal 828,000, you first need to find out what half of 828,000 is. 828,000/2=414,000. for the two numbers to equal 828,000, you have to add the same amount as you subtract from the middle. in this case, the number is 9,000 because it's half of 18,000. to equal 828,000, you have to add 9,000 to 414,000 for the camry and subtract 9,000 from 414,000 for the accord. 414,000+9,000=423,000.

414,000-9,000=405,000.

423,000+405,000=828,000.

423,000-405,000=18,

hope it