Given (2, 10) and (3, 4), find the slope.

Understand the Problem

The question is asking to calculate the slope of a line given two points: (2, 10) and (3, 4). The slope can be found using the formula (y2 - y1) / (x2 - x1).

Answer

The slope of the line is $-6$.

Steps to Solve

Identify the points The two points given are (2, 10) and (3, 4). Here, we have:

Point 1: $(x_1, y_1) = (2, 10)$
Point 2: $(x_2, y_2) = (3, 4)$

Use the slope formula The formula for the slope $m$ of a line through two points is given by:

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

Substitute the values Now, substitute the values from the points into the formula:

$$ m = \frac{4 - 10}{3 - 2} $$

Calculate the difference in the y-coordinates Calculate $y_2 - y_1$:

$$ 4 - 10 = -6 $$

Calculate the difference in the x-coordinates Calculate $x_2 - x_1$:

$$ 3 - 2 = 1 $$

Compute the slope Now substitute these differences back into the slope formula:

$$ m = \frac{-6}{1} = -6 $$

The slope of the line is $-6$.

More Information

The slope represents how steep the line is, and a negative slope indicates that the line is decreasing from left to right.

Tips

Forgetting to subtract the coordinates in the correct order can lead to an incorrect slope value. Always remember that the formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
Confusing $x$ and $y$ coordinates when plugging them into the formula.

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