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kupik [55]
3 years ago
8

Find the slope of the line that passes through (4,2) and (9,1)?

Mathematics
2 answers:
pshichka [43]3 years ago
8 0

Answer:

The slope of the line is \displaystyle -\frac{1}{5}.

Step-by-step explanation:

We are given two coordinate points:

  • (4, 2)
  • (9, 1)

We are asked to find the slope of the line.

We can use the rise-over-run formula to solve for the slope of the line.

\displaystyle \text{slope} = \frac{\text{rise}}{\text{run}}\\\\\text{slope} = \frac{y_2-y_1}{x_2-x_1}

However, we firstly need to name our coordinate points.

In math, we can label our coordinates using the following label system:

(x_1, y_1), (x_2, y_2)

Therefore, we can also label our coordinates as such:

  • x_1 = 4
  • y_1 = 2
  • x_2 = 9
  • y_2 = 1

Now, we can supply these values into the formula and solve for our slope, or a better known variable, <em>m</em>.

\displaystyle m = \frac{1 - 2}{9 - 4}\\\\m = \frac{-1}{5}\\\\m = -\frac{1}{5}

Therefore, our slope is \displaystyle -\frac{1}{5}.

Nataly [62]3 years ago
8 0

Answer: m= -1/5

Step-by-step explanation:

<em>Find the Slope </em>(4, 2) <em>and </em>(9, 1)

<em>Slope is equal to the change in y over the change in x, or rise over run.</em>

              change in y

     m =    _________

              change in x

<em>The change in x is equal to the difference in x-coordinates (also called run), and the change in y is equal to the difference in y-coordinates (also called rise).</em>        y₂ − y₁

     m =   _____

              x₂ − x₁

<em>Substitute in the values of x and y into the equation to find the slope.</em>

              1 − (2)

     m =   _____

              9 − (4)

<em>Simplify the numerator.</em>

                −1

     m =   _____

              9 − (4)

<em>Simplify the denominator.</em>

                −1

     m =   _____

                 5

<em>Move the negative in front of the fraction.</em>

                −1

     m =   _____

               − 5

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Farmer Bill sold potatoes at the farm market. He sold a quarter to the first person, 4/9 of what was left to the second person,
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Answer: 120 lb of potatoes.

Step-by-step explanation:

Let the pounds of potatoes sold by farmer Bill      = X lb

Fractional part sold to the first person                    = 1/4

Therefore 1/4 of X                                                      = 1/4  x X

                                                                                    = X/4 lb of potatoes.

No of potatoes left for sale                                        = X - X/4

                                                                                    = ( 4x - x )/4

                                                                                    = 3x/4 lb.

Fractional part sold to the second person out of the reminder = 4/9

Therefore 4/9 of 3x/4                                                 = 4/9 x 3x/4

                                                                                    = x/3 lb of potatoes.

Amount of potatoes left for sale                               = 3x/4 - x/3

Resolve into fraction , we have                                 = (9x - 4x)/12, because 12 is the LCM.

                                                                                    = 5x/12

Third buyer bought 4/5 of the left over                    = 4/5 of 5x/12

                                                                                   =   x/3 lb of potatoes.

Amount  of potatoes left                                           =   5x/12 - x/3

Resolve in to fraction again  taking 12 as the LCM =   ( 5x - 4x )/12

                                                                                   = x/12 lb of potatoes .

Therefore, the left over was 10 lb .

To determine the value of x now which correspond to the amount of potatoes sold by Farmer Bill, we shall the equate the left to  x/12 = 10                                                                                                                

we now cross multiply to get the value of x                             x = 120 lb.

therefore the pound of potatoes sold by farmer Bill  = 120 lb.                                        

                                                                                 

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