Mathematics: Carlota wrote the equation y + 1 = 2 (x - 3) for the line passing through the points (-1, 3) and (2, 9). explain and correct her error.

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Carlota wrote the equation y + 1 = 2 (x - 3) - id123558432, FlowerChild5037

crosales102

11.03.2022

For this case we have the following equation:

y + 1 = 2 (x - 3)

That can be rewritten in the form y = mx + b

Where:

m is the slope of the line b is the cut point

So, we have:

$y + 1 = 2 (x - 3)\\y + 1 = 2x-6\\y = 2x-6-1\\y = 2x-7$

Where:

m = 2 is the slope

b = -7 is the cut point

Carlota has the following points:

(-1, 3) and (2, 9)

To know if the line y = 2x-7 passes through these points, we must replace them in the equation and the equality must be fulfilled. So:

Point (-1, 3):

Substituting:

$3 = 2 (-1) -7\\3 = -2-7$

3 = -9 It's false, equality is not met. The point (-1, 3) does not go through the line.

The equation written by Carlota is erroneous, the procedure to follow is:

Given (x1, y1) = (- 1, 3) and (x2, y2) = (2, 9) , we find the slope:

$m=\frac{(y2-y1)}{(x2-x1)}$

$m=\frac{(9-3)}{(2-(-1))}$

$m=\frac{6}{3}$

m=2

We observe that the slope found by Carlota is the same. Let's see cut point "b". For this we substitute any of the points given in the equation:

y = 2x + b

Substituting (2,9) we have:

$9 = 2 (2) + b\\9 = 4 + b\\b = 9-4\\b = 5$

Thus, Carlota's error was at the cut-off point. The correct equation of the line that passes through the given points is y = 2x + 5

The correct equation of the line that passes through the given points is y = 2x + 5

Carlota's mistake was at the cutoff point

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