Hi

Find the slope and y-intercept of the line in the given equation y=4/9x-20

 



y = (4/9)x-20  |slope= 4/9 and y-intercept is Pt(0,-20)

Hi

find the linear equation passing through the given point: (0,3) (4,7)

Using the point-slope formula, 

(0,3) 

(4,7) m = -4/-4 = 1

 



 y = x + b   |using ordered pair Pt(0,3) to solve for b

 3 = 0 + b

 3 = b 

 y = x + 3 |written in slope-intercept form

Hi

line that passes through (-4, 0) and is parallel to y= -2x+1

 



y= -2x+1   |slope m = -2.  Parallel lines have identical slopes  

New Line: m = -1/3   |Note: 3*-1/3 = -1

 y = -2x + b   |using ordered pair Pt(-4,0) to solve for b

 0 = 8 + b

 -8 = b 

 y = -2x -8  |written in slope-intercept form

Hi

line that passes through (3, -2) and is perpendicular to y=3x-4 



y=3x-4    |slope m = 3  

perpendicular lines have slopes that are neagtive reciprocals of one another

New Line: m = -1/3   |Note: 3*-1/3 = -1

 y = (-1/3)x + b   |using ordered pair Pt(3,-2) to solve for b

-2 = -1 + b

 -1 = b 

 y = (-1/3)x - 1 |written in slope-intercept form

Hi

line that passes through (-2, 3) and is perpendicular to 2x – 9y = -12 

 



2x – 9y = -12 OR y = (2/9)x + 12/9  |slope m = 2/9.  

perpendicular lines have slopes that are neagtive reciprocals of one another

New Line: m = -9/2   |Note: 2/9*-9/2 = -1

 y = (-9/2)x + b   |using ordered pair Pt(-2,3) to solve for b

 3 = 9 + b

 -6 = b 

  y = (-9/2)x -6  |written in slope-intercept form

Hi



A line that passes through the origin and is parallel to x + y = 6.

 



 x + y = 6  OR y = -x + 6  |slope m = -1.  Parallel lines have identical slopes

New Line:

 y = -x + b   |using ordered pair Pt(0,0) to solve for b

 0 = 0 + b

 0 = b 

  y = -x   |written in standard from: x + y = 0

Hi

Write the slope-intercept equation for the line that passes through 

(4, -9) and has slope -3/4. 

 



 y = (-3/4)x + b   |using ordered pair Pt(4,-9) to solve for b

-9 = -3 + b

-6 = b 

  y = (-3/4)x -6    |written in the slope-intercept form

Hi

Write the standard form of the equation of the line through the pair of points (5,-5) and (-6,10). 

Using the point-slope formula, 

( 5,-5) and 

(-6,10)  m = -15/11

 



  y = (-15/11)x + b  \using ordered pair Pt(5,-5) to solve for b

 -5 = -75/11 + b

 20/11 = b

  y = (-15/11)x + 20/11  OR 15x + 11y = 20

Hi

Using the point-slope formula, 

(2,9) and 

(1,4)  m = 5/1 Or m = 5

Hi

solving by the elimination method

14x+18y=-54

-4x-14y =42



  14x  +18y=- 54

-36/7x -18y = 54   |Multiplying 2nd Equation by 9/7, adding and eliminating y

    x = 0  and y = -3   | 14*0 + 18y = -54  OR y = -3



CHECKING our Answer***

-4x-14y =42

 0 -14*-3 = 42

Hi

solving by the elimination method

  x+2y=11

12x-6y=12



 3x+6y=33    |multiplying the 1st equation by 3, adding and eliminating y

12x-6y=12

   15x = 45   x = 3 and y = 4   | x+2y=11 OR 2y = 11-3 OR 2y = 8 & y = 4



CHECKING our Answer***

 12x -  6y  = 12

 12*3 - 6*4 = 36 -24 = 12

Hi

solving by the elimination method

 -2x+3y=14

  x+2y=7



-2x+3y=14

 2x+4y=14       |Multiplying 2nd quation by 2, adding and eliminating x

    7y = 28   y = 4  and x = -1     | x+2y=7  OR x= 7- 2*4



CHECKING our Answer***

 -2x + 3y =14

  -2(-1) + 3*4 = 2 + 12 = 14

Hi

Half the difference of four and a number increased by three

Let n represent the number

the Expression of this in terms of n would be:  

 [4 -(n+3)]/2  OR (1-n)/2

Hi

y decreased by the product of 19 and y

the Expression of this in terms of y would be:  y - 19y

Hi

the number of weeks in k years.  (52 weeks in one year)

translate into algebraic expression:  52k

Hi

Note: first quadrant is of the form (x, y), where x > 0 and y > 0

Hi

Using the vertex form of a parabola,  where(h,k) is the vertex

Sketching the first-quadrant portions of y=x^2+8x+16

 y = x^2+8x+16

 y= (x+4)^2 - 16 + 16

 y = (x+4)^2  |When x = 0, then y = 16

Cannot demonstrate here, however it would be the portion of the parabola

in the first-quadrant

Hi

(x + 1)(x – 2) = 54    

This equation states it is the PRODUCT of (x+1) and (x-2) = 54!

Note: The factor theorem states that a polynomial f(x) has a factor (x − k)

where k is a 'solution' if and only if f(k) = 0

(x + 1)(x – 2) = 54  |Putting this in the form ax^2 + bx + c = 0 in order to factor

 x^2 -x - 2 = 54

 x^2 -x - 56 = 0     |Yes!

factoring

 (x-8)(x+7)= 0       |NOW! 'Each' of the Products is = 0

  (x-8)= 0   x = 8

  (x+7)= 0   x = -7



CHECKING our Answer(s)***

(x + 1)(x – 2) = 54 

  9*6 = 54

 -6*-9 =54

Hi

range of the function  y= x^2    |Note use of ^ (uppercase 6)

Range of y is [0,)

Hi

Note:

 log(x)+log(x)=2

 log(x^2)=2



  10^2 = x^2

    x = 10       |(Note: -10 is an Extraneous solution)



CHECKING our Answer***

 log 10 + log 10 = 1 + 1 = 2

Hi

twice the first number is one more than the second.

Let x and (2x -1)represent the first and  second number respectively

Question states***

 x + (2x -1)= -64

Solving for x

    3x = -63

     x = -21, the first number.  The second number is -43  (-42-1)

CHECKING our Answer***

 -21 + (-43) = -64

Hi

Pablos age is 5 more than 3 times his son's age

If son's age is represented by "s"

Pablos age = 3s + 5

Hi

Writing each decimal as a fraction or mixed number.

 .65 = 65/100 = 13/20

5.035 = 5 35/1000 = 5 7/200

Hi

solving "Linear system using substitution"

4x-y=17  OR y = 4x-17 |Need to solve for one variable in either equation 

-9x+8y=2              |subsituting for y

 -9x + 8(4x-17) = 2

 -9x + 32x - 136 = 2

        23x = 138

          x = 6  and y = 7  (4*6 -17) Ordered pair Pt(6,7) is the solution

CHECKING our Answer***

 -9x + 8y =2

 -54 + 56 = 2

Hi

 



Line passing thru Pt(-3,0) with slope of 1/2

 y = (1/2)x + b   |using ordered pair pt(-3,0) to solve for b

 0 = -3/2 + b

 3/2 = b  

 y = (1/2)x + 3/2  

 

Hi

one of the integers is five less than seven times the other integer.

Let x and (7x-5)represent the intergers

Question states***

 x(7x-5) = 408

   7x^2 - 5x -408 = 0

Solving for x









   x = 112/14 = 8  and x = -102/14 (extraneous solution as is a non-integer)  

Integers are 8 and 51 (7*8-5)



CHECKING our Answer***

   8*51 =408

Hi

Solving  by substitution method

x = 24 - 4y

4x + 3y = -8

4(24-4y) + 3y = -8

 96 - 16y + 3y = -8

     104 = 13y   

      8 = y  &  x = 24-4y = -8   Ordered pair (-8,8)is the solution



CHECKING our Answer***

 4x + 3y = -8

-32 + 24 = -8



      

Hi

sketching parabola: Format: (y-k)^2 = 4p(x-h)

I. Vertex is Pt(0,0)

II. Opens left.  Line of symmetry is the x-axis

III. Directrix is x = 5  -p = 5  OR p = -5  and 4p = -20

 y^2 = -20x   OR  x = (-1/20)y^2

Hi

Let x represent the score of his 3rd game

 (147 + 186 + x)/3 ≥ 170

  (147 + 186 + x) ≥ 510

           x  ≥ 177   Must bowl 177 or more

Hi

Express in terms of i and show any work. 

-sqrt(-496) = -isqrt(16*31) = -4isqrt(31)

 

Hi

solving for x

(7x-3)+ 77+50= 180

 7x-3+ 77+50= 180

 7x - 3 = 53

   7x = 56

    x = 8   |Good work