# MAT 1304

MAT 1304 10

MAT1304

1.Findthe slope of the line through the following pair of points using theslope formula.(-2, -4) and (-11, -2) select the correct choicebelow, and if necessary, fill in the answer box to complete yourchoice.

Slope= change in Y/change in x

=(-2+4)/ (-11+2)

=-2/9a. The slope of the line is -2/92.Find theslope of the line if it is defined.Through (7, 9) and (7, -7)

Slope= (9+7)/7-7

17/0= ∞b. The slope is undefined.3. Find the slope,if it exists Select the correct choice below and fill in any answerboxes within your choice.3x-7y =14

Thisequation expressed in form of Y = mx + c will be as follows

7y= 3x -14

Y= 3/7x -2a. The slope is 3/74.Find the slope of thelineY=17This is the same rewriting the equation as y = 0x+ 17 the value of m = 0 implying the slope is 0a. The slope is0 (zero)5.Find an equation of the line having the givenslope and containing the given pointM = -7, (6, 9)Theequation of the line is y = (simplify your answer. Type your answerin slope-intercept form. Use integers or fractions for any numbers inthe expression.)

(Y– 9)/(x – 6) = -7

Y– 9 = -7(x – 6)

Y– 9 = -7x + 42

Y= -7x + 51

6.Find an equation of the line that contains the following pair ofpoints.The equation of the line is.(3, 2) and (1, 5)(simplify your answer. Type your answer in slope-intercept form. Donot factor)Slope = (5 – 2)/1-3

=-1.5

Equationof the line (y – 5)/(x – 1) = -1.5

Y– 5 = -1.5 (x – 1)

Y= -1.5x + 1.5 + 5

Y= -1.5x + 6.5

7.Find an equation for the given line in the form ax + by = c, where a,b, c are integers with no factor common to all three and a _&gt_0.Through (-8, 10) parallel to 5x + 4y = 17 The equationof the line in the form ax + by = c, passing through (-8, 10) andparallel to 5x + 4y = 17 is. (Simplify your answer.)

Slopeof the line 5x + 4y = 17 is -5/4 since the equation can be expressedas y = -5/4x + 17/4

Becausethe lines are parallel to each other, it implies they have the samegradient. Therefore, the equation of the line would be

(y– 10)/(x + 8) = -5/4

4(y-10)= -5 (x + 8)

4y– 40 = -5x – 40

Writtenin the form of ax + by = c it would be as follows

5x+ 4y = 0

9.Write an equation in standard form for the line describedThrough(7, 8), perpendicular to 8x + y = 2The equation of the line isx â + () y = ()

Thegradient of the given line is -8 since y = -8x + 2Because thelines are perpendicular, then the gradient of the other line is 1/8

Therefore,the equation of the line is as follows

(Y– 8)/ (x -7) = 1/8

8(y– 8) = x – 7

8y– 64 = x – 7

8y– x = 57

Instandard form -x + 8y = 5712. Graph the followingequation.7x + 4y = – 28Use the graphing tool to graph theequation.13.In 1999, there were 41,744 shopping centers in a certain country. In2009 there were 48,937.a. Write an equation expressingthe number y of shopping centers in terms of the number x of yearsafter 1999.

(48,937– 41,744)/ (2009 – 1999)

=7193/ 10

=719.3b.When will the number of shopping centers reach 80,000?(80,000 –48,937)/ x – 2009 = 719.3

31063= 719.3 (x – 2009)

31063= 719.3x – 1,445,073.7

719.3x= 1476136.7

X= 2052.2

Therefore,shopping centers will reach 80,000 in 2052

14.Let f(x) = 5 -3x. Find f (-5).F (-5) = 5 – 3 (-5)

=5 + 15=2015. Let g(x) = 6x -3. Find g (- ½)g(- ½) = Type an integer or a fraction.If g(x) = 6x –3, then g(-1/2) will be

6^-0.5– 3

=0.41– 3

=-2.59

16.Write a linear cost function for the following situation.A skiresort charges a snowboard rental fee of \$20 plus \$2.25 per hour.C(t) = (2.25) t+ 2017. Assume that the situation can beexpressed as a linear cost function. Find the cost function.Fixedcost is \$100 50 items cost \$2,100 to produce. The linear costfunction is C(x) = ().Variable cost = 2100 and fixed cost =100. In this case, X = 50

C(50)= 2100 + 100

C(50)= \$220018. The dispatch tool works spends \$32000 toproduce 140 parts, achieving a marginal cost of \$210. Find the linearcost function.

Marginalcost implies producing one more part would cost \$210 therefore,producing 140 parts would cost 140*210 = 29,400

Fixedcost = 32000 – 29400 = 2,600The linear cost function is C(x)= (210) x + 260019. Use the information listedbelow to solve parts a through h.Supposed that the demand andprice for a certain model of a youth wristwatch are related by thefollowing equation. P = D (q) = 24 – 1.25q.Where p is the price(in dollars) and q is the quantity demanded (in hundreds). Find theprice at each level of demand. Answer parts a through d.a.Findthe price when the demand is 0 watches.

Whenq = 0 P = 24 – 1.25 (0)

P= 24 dollarsThe price when the demand is 0 watches is \$ 2421.Joan sells silk-screened T-shirts at community festivals and craftsfairs. Her marginal costs to produce one T-shirt is \$2.50. Her totalcost to produce 40 T-shirts is \$150, and she sells them for \$6each.Find the linear cost function for Joanne’s T-shirtproduction.

Y– 150 = 2.50 (x – 40)

Y= 2.50x + 150 – 100

Y= 2.50x + 50

C(x)= 2.50x + 50

Howmany T-shirts must she produce and sell in order to break even?

Atbreak-even TR = TC

6x= 2.5x + 50

3.5x=50

X= 14.3

Howmany T-shirts must she produce and sell to make a profit of \$700?

Profit= TR- TC

700= 6x – (2.50x + 50)

700= 6x – 2.5x -50

750= 3.5xx = 214.322. To produce xunits of a religious medal costs C(x) = 16x + 78. The revenue is R(x)= 29x. Both cost and revenue are in dollars.Find thebreak-even quantity.

TC=TR

16x+78 = 29x

13x= 78

X= 6

Break-evenquantity = 6 units

Findthe profit from 440 units.

Profit= TR – TC

29(440)– (16(440) + 78)

12760– 7040 – 78

=5642 dollarsFind the number of units that must be produced fora profit of \$130.

Profitfunction = 29x – (16x +78)

=13x – 78130 = 13x -78

13x= 208

X= 16

=16 units23. A product has a production costfunction C(x) = 150x + 4350 and a revenue function R(x) = 200x. Findand analyze the break-even quantity, then find the profit function.Answer parts a and b below.

AtBreak-even, TR = TC 200x = 150x + 4350

50x= 4350

X= 87The break-even quantity is 87 units.Profitfunction = TR – TC

=200x – (150x + 4350)

=200x– 150x – 4350

=50x – 435024. Use the formula C=5/9(F -32) for conversionbetween Fahrenheit and Celsius to convert each temperature.a.75 degrees F to Celsius

C= 5/9 (75 -32)

C= 5/9 (47)

C= 26.11

=26.1degrees C

b.-30 degrees F to Celsius

C= 5/9 (-30 -32)

C= 5/9 (-62)

=-34.4 degrees Cc.30 degrees C to Fahrenheit

30= 5/9 (F – 32)

270= 5F – 160

5F= 430

F= 86

=86 degrees F