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goldfiish [28.3K]
3 years ago
11

when a linear function is graphed it passes through the points (-1,1), (1,5), and (3,9) what is the rate of change for the funct

ion?
Mathematics
1 answer:
vesna_86 [32]3 years ago
5 0
Use the linear slope formula to solve for m: 

m=(y2-y1)/(x2-x1)

using the points (-1,1) and (1,5) you can find the slope for the first interval:
 
m=(5-1)/(1-(-1))
m=4/2
m=2

you can double check by using the same formula on the second interval, which is (1,5) to (3,9).

m=(9-5)/(3-1)
m=4/2
m=2 

therefore, the rate of change is 2. 
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Find the equation of the linethe line passes through the points (5,2) and (-4,-4)
almond37 [142]

Answer:

y =  \frac{2}{3}x -  \frac{4}{3}

Step-by-step explanation:

first find the slope using the above points then use the slope formula to calculate the slope

m =  \frac{y2 - y1}{x2 - x1}  \\  \frac{2 - -  4}{5 -  - 4}  =  \frac{2 + 4}{5 + 4}  =  \frac{6}{9}  =  \frac{2}{3}

substitute ⅔ for m and one of the above points into the y-intercept form of the equation for a line and solve for b

y = mx + b \\ 2 =  \frac{2}{3} (5)  + b \\ 2 =  \frac{10}{3}  + b \\ 2 -  \frac{10}{3}  = b \\  \frac{6}{3}  -  \frac{10}{3}  = b \\ b =  -  \frac{4}{3}

substitute the slope and the value for b into the equation to get the answer

y =   \frac{2}{3} x -  \frac{4}{3}

4 0
3 years ago
Find the distance between the points (8,1) and (2,10).<br> Round decimals to the nearest tenth.
miss Akunina [59]

The nearest distance between the points (8,1) and (2,10) is 11 units, which is mentioned in and also calculated by using formula.

Step-by-step explanation:

The given is,

             Two points are (8,1) (2,10)

Step: 1

            By graphical method, refer the attachment,

                    First point (8,1)

                           The values of x=8 and y=1 noted in the graph

                    Second point (2,10)

                          The values of x=2 and y=10 noted in the graph

            Now join the two points (8,1) and (2,10)

                          Measure the distance between two points, the distance is 11 units. Due to some error the value becomes 10.98 or 11.1 we need to convert the answer into nearest whole number.

                                                     ( OR )

Step:1

        By formula method,

                   Distance =  \sqrt{(x_{2} - x_{1} )^{2} +(y_{2} - y_{1} )^{2} }.....................(1)

        Where,

                    (8,1) are (x_{1},y_{1})

                    (2,10) are (x_{2},y_{2})

       From the equation,

                                 = \sqrt{(2 - 8 )^{2} +(10 - 1 )^{2} }

                                 = \sqrt{(-6 )^{2} +(9 )^{2} }

                                 = \sqrt{36 +81 }

                                  = \sqrt{117}

                                  = 10.81665

                                  ≅ 11             ( Answer convert to the nearest tenth)

                  Distance = 11 units

Result:

               The nearest distance between the points (8,1) and (2,10) is 11 units, which is mentioned in and also calculated by using formula.

5 0
3 years ago
Need help with number 16
dlinn [17]
I would go with B x= -5
8 0
3 years ago
Help me
Katarina [22]
The answer is 5

9+6 = 15
15/3 is 5
4 0
3 years ago
Read 2 more answers
Find the inverse of the following function. f(x) =^3squareroot x + 12<br><br> I NEED AN ANSWER NOWW
makkiz [27]

Answer:

(x - 12)²/9

Step-by-step explanation:

y = 3sqr(x) + 12

Make x the subject:

y - 12 = 3sqrt(x)

(y - 12)/3 = sqrt(x)

Square both sides

(y - 12)²/9 = x

Interswitch variables

inverse function is:

(x - 12)²/9

If f(x) = (x + 12)^⅓

Then,

y = (x + 12)⅓

y³ = x + 12

y³ - 12 = x

f inverse:

x³ - 12

3 0
3 years ago
Read 2 more answers
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