What is the y-intercept of the line perpendicular to the line y = 3/4x + 3 that includes the point (3, 1)?

a. -5/4

b. 3

c. -13/4

d. 5

  D.  5

Step-by-step explanation:

The attached shows a graph of the line in point-slope form. It has a y-intercept of 5.

The slope of the given line is 3/4. The slope of the perpendicular line will be the negative reciprocal of that: -1/(3/4) = -4/3.

The point-slope form of the equation of a line with slope m through point (h, k) can be written ...

  y = m(x -h) +k

For the desired slope and given point, this equation is ...

  y = (-4/3)(x -3) +1 = (-4/3)x +4 +1

  y = (-4/3)x +5 . . . . . equation in slope-intercept form

The y-intercept is seen to be 5.

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5