Question

Find the Error A student finds the slope of the line that passes through the points (-3,8) and (2,-4). Find the mistake and correct it. m=(-3-8)/(2-(-4)) m=(-11)/(6)

Answer 1

The student used a wrong formula to calculate the slope of the line. The slope is: -2.

How to Calculate the Slope of a Line?

The slope of a line is the change in y / change in x, which is the rise of the line over the run of the line. The formula for the slope can be expressed as:

m = $\frac{y_2 - y_1}{x_2 - x_1}$.

Given that a line passes through the points (-3,8) and (2,-4), to find the slope of the line, let:

(-3, 8) = $(x_1, y_1)$

(2, -4) = $(x_2, y_2)$

Substitute the values into m = $\frac{y_2 - y_1}{x_2 - x_1}$.:

Slope of the line (m) = $\frac{y_2 - y_1}{x_2 - x_1}$ = (-4 - 8)/(2 - (-4)) [this is where student made a mistake, he didn't apply the correct slope formula that should be used to find the slope of a line]

Slope of the line (m) = -12/6

Slope of the line (m) = -2

Therefore, we can conclude that the student got a wrong slope value because he didn't apply the right slope formula that is used to find the slope of any given line. The slope for the line should be -2 instead of -11/6.

Learn more about slope of a line on:

https://brainly.com/question/16949303

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Answer 2

Answer:

They used the wrong formula, correct answer: -2.4

Step-by-step explanation:

The slope of a linear line, can be calculated using the formula: $\frac{y_2-y_1}{x_2-x_1}$

Which can intuitively be understand, by realizing the definition of a slope is also generally defined as: $\frac{\text{change in y}}{\text{change in x}}$.

So the  $\text{change in y} = y_2 - y_1$ and the $\text{change in x} = x_2-x_1$, and we just substitute these algebraic expressions to derive the slope formula.

Let's assign values to the x and y values as such:

$(x_1, y_1) = (2, -4)\\(x_2, y_2) = (-3, 8)$

Note: We could've assigned the values as such: $(x_1, y_1) = (-3, 8)\\(x_2, y_2) = (2, -4)$

and we would get the same slope, we just have to be consistent with how we plug in the x and y values.

from here we can substitute values into the equation to get:

$m=\frac{8-(-4)}{-3-2}$

Now we can spot the error the student made. They used the wrong formula. The formula they used: $\frac{x_2-y_2}{x_1-y_1}$, as explained above, we can derive the slope formula by the common definition. This formula being used isn't finding the change in x and y, just the difference between the x and y coordinates.

If the student applied the formula correctly they would get the equation we got above.

We can further simplify the equation:

$m=\frac{8-(-4)}{-3-2}$

To the following:

  $m=\frac{8+4}{-5}$

From here simplify the numerator further:

$m=\frac{12}{-5}$

Which in decimal form is

$m=-2.4$