Question

Misty correctly determined the equation of the linear function represented by the table of values below to be y = negative 2 x + 9 in slope-intercept form by using the ordered pairs (1, 7) and (2, 5).
What would she have gotten for the equation of the linear function if she had used the ordered pairs (2, 5) and (4, 1) instead?

Answer 1

SOLUTION

GIVEN

Misty correctly determined the equation of the linear function represented by the table of values below to be y = - 2 x + 9 in slope-intercept form by using the ordered pairs (1, 7) and (2, 5).

TO DETERMINE

The equation of the linear function if she had used the ordered pairs (2, 5) and (4, 1) instead

EVALUATION

First we verify the answer of Misty

Mistry has find the equation of the linear function represented by the table of values below to be y = - 2 x + 9 in slope-intercept form by using the ordered pairs (1, 7) and (2, 5).

So the given equation of the linear equation is

$\sf{y = - 2x + 9} \: \: ....(1)$

Putting x = 1 & y = 7 in Equation (1) we get

$\sf{7 = (- 2 \times 1) + 9}$

$\implies \sf{7 = 7}$

Again putting x = 2 & y = 5 in Equation (1) we get

$\sf{5 = ( - 2 \times 2) + 9}$

$\implies \sf{5 = 5}$

Hence Misty has correctly determined the equation of the linear function

Now if Misty has used the ordered pairs (2, 5) and (4, 1) instead

Then the equation of the Linear function can be determined as below

$\displaystyle \sf{ \frac{y - 5}{x - 2} = \frac{1 - 5}{4 - 2} }$

$\implies \displaystyle \sf{ \frac{y - 5}{x - 2} = \frac{ - 4}{2} }$

$\implies \displaystyle \sf{ \frac{y - 5}{x - 2} = - 2}$

$\implies \displaystyle \sf{y - 5 = -2 x + 4}$

$\implies \displaystyle \sf{y = -2 x + 9}$

Therefore equation of the linear equation is same as before

JUSTIFICATION FOR SAME ANSWER

Since the points (1, 7), (2, 5) & (4, 1) are collinear

For this reason the equation of the linear equation is same

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Answer 2

Answer:

y = negative 2 x + 9

Step-by-step explanation:

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