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Find the equation of the linear function passing through (2,3) and (5,12)

Elis [28]

y = 3x - 3 is the equation of the linear function passing through (2, 3) and (5, 12)

Solution:

Given that we have to find the equation of linear function passing through (2, 3) and (5, 12)

The formula y = mx + b is said to be a linear function

Where "m" is the slope of line and "b" is the y - intercept

Let us first find the slope of line

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text {Here } x_{1}=2 ; y_{1}=3 ; x_{2}=5 ; y_{2}=12$

Substituting values we get,

$m=\frac{12-3}{5-2}=\frac{9}{3}=3$

Thus slope of line is m = 3

To find the y - intercept, substitute m = 3 and (x, y) = (2, 3) in y = mx + b

3 = 3(2) + b

3 = 6 + b

b = 3 - 6

b = -3

Thus the required equation of linear function is:

Substitute m = 3 and b = -3 in formula

y = mx + b

y = 3x - 3

Thus the equation of linear function is found

6 0

3 years ago

I. In a shipment of 300 connecting rods, the mean tensile strength is found to be 45 kpsi and has a standard deviation of 5 kpsi

CaHeK987 [17]

Answer:

a) Between 39 and 40 rods can be expected to have a strength less than 39.4 kpsi.

b) 260 rods are expected to have a strength between 39.4 and 60 kpsi

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 45, \sigma = 5$

(a) Assuming a normal distribution, how many rods can be expected to have a strength less than 39.4 kpsi?

The percentage of rods with a stength less than 39.4 is the pvalue of Z when X = 39.4. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{39.4 - 45}{5}$

$Z = -1.12$

$Z = -1.12$ has a pvalue of 0.1314

13.14% of rods have a strength less than 39.4 kpsi.

Out of 300

0.1314*300 = 39.42

Between 39 and 40 rods can be expected to have a strength less than 39.4 kpsi.

(b) How many are expected to have a strength between 39.4 and 60 kpsi?

The percentage of rods with a stength in this interval is the pvalue of Z when X = 60 subtracted by the pvalue of Z when X = 39.4. So

X = 60

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{60 - 45}{5}$

$Z = 3$

$Z = 3$ has a pvalue of 0.9987

X = 39.4

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{39.4 - 45}{5}$

$Z = -1.12$

$Z = -1.12$ has a pvalue of 0.1314

0.9987 - 0.1314 = 0.8673

86.73% of the rods are expected to have a strength between 39.4 and 60 kpsi

Out of 300

0.8673*300 = 260

260 rods are expected to have a strength between 39.4 and 60 kpsi

4 0

4 years ago

Marcia has a sunflower garden. The plants are currently 36 inches tall and are growing at a rate of 4 inches each week. Write an

Lady_Fox [76]

I believe the correct answer from the choices listed above is the last option. The equation that would represent the height of the sunflower plants would be H = 4w + 36 where the initial height of 36 signifies the b in the equation. and the rate 4 is the slope m.

Hope this answers the question. Have a nice day.

8 0

4 years ago

Solveing systems of equations by substitution y=6x-11 -2x-3y=-7

sergiy2304 [10]

$\bf \begin{cases} \boxed{y}=6x-11\\ \cline{1-1} -2x-3y=-7 \end{cases}\qquad \implies \stackrel{\textit{substituting \underline{y} in the 2nd equation}}{-2x-3\left( \boxed{6x-11} \right)=-7}$

$\bf -2x-18x+33=-7\implies -20x+33=-7\implies -20x=-40 \\\\\\ x=\cfrac{-40}{-20}\implies \blacktriangleright x=2 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that }}{y=6x-11}\implies y=6(2)-11\implies y=12-11\implies \blacktriangleright y=1 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (2,1)~\hfill$

7 0

3 years ago

Read 2 more answers

1. Between which two perfect squares is √130? 2. Which two integers is √82 between?

max2010maxim [7]

Q1:-
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12*12= 144
11*11=121
so the answer of 1. lies between 11 and 12

Q2:-
--------
9*9=81
10*10=100
so sqrt(82) is between 9 and 10

5 0

3 years ago

Read 2 more answers