geno3141

To calculate the x-intercept, put 0 in for y:  0  =  5x - 4   -->   4  =  5x   -->  x  =  4/5

To calculate the y-intercept, put 0 in for x:  y  =  5(0) - 4   -->  y  =  -4

The total number of combinations of 25 out of 37 sold is:  37nCr25

Choosing 1 out of 2 defective:  2nCr1

Choosing 24 out of 35 good:  35nCr24

Probability:   [ 2nCr1 · 35nCr24 ] / 37nCr25

Choose three numbers for x; I'll choose:  x = -2, x = 0, and x = 2

    x  |  y

---------

  -2  |                            Solve:  y  =  -2(-2) + 2  --->   y  =  4 + 2  --->  y  =  6

   0  |                            Solve:  y  =  -2(0) + 2  --->  y  =  2

   2  |                            Solve:  y  =  -2(2) + 2  --->  y  =  -4 + 2  --->  y  =  -2

Place these y-values into the table; plot the points, and draw the line.

If an example of your question is:  given that a line passes through the point (5,6), find the equation of the line 

Can't be done; not enough information.

If you know something else, like the slope, it can be done.

My answer would be:

---   to solve a problem algebraically, you use an equation, involving one or more unknowns;

---   to solve a problem arithmetically, you don't write an equation.

Example:

If 5 dogs eat 10 pounds of dog food , how many dogs (same size) would it take to eat 40 pounds of dog food?

Algebraically:  5/10  =  x/40   --->   cross multiply   --->   10x  =  200   --->   x  =  20 dogs.

Arithmetically: Think this way: if 5 dogs ate 10 pounds, each dog ate 2 pounds, and 40 / 2  =  20 dogs. 

They were good!  (Burp!)

                        y  =  -2x + 16

Since  x = 6:    y  =  -2(6) + 16    =    -12 + 16    =    4

    (6, 4)

Get a common denominator:

     27  =  3x3x3

     18  =  2x3x3

     10  =  2x5

Lowest common denominator:  2x3x3x3x5  =  270

19/27:    since 27 goes into 270 10 times, multiply by 10/10  to get  190/270

5/18:      since 18 goes into 270 15 times, multiply by 15/15 to get 75/270

1/10:      since 10 goes into 270 27 times, multipoly by 27/27 to get 27/270

19/27 + 5/18 + (-1/10)    becomes    190/270 + 75/270 + (-27/270)    =    238/270    =  119/135

Solve it for y.

For example:                                2x + 3y  =  6

Subtract 2x from both sides:               3y  =  -2x + 6

Divide both sides by 3:                          y  =  -2/3·x + 3

Slope  =  -2/3

Y-intercept  =  3