To find the slope of the line that passes through the points (10, 4) and (7, 3), we will use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points. Here, [tex]\((x_1, y_1) = (10, 4)\)[/tex] and [tex]\((x_2, y_2) = (7, 3)\)[/tex].
Step-by-Step Solution:
1. Identify the coordinates:
[tex]\[ x_1 = 10, \quad y_1 = 4, \quad x_2 = 7, \quad y_2 = 3 \][/tex]
2. Substitute the coordinates into the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 4}{7 - 10} \][/tex]
3. Perform the subtraction in the numerator (y-coordinates):
[tex]\[ 3 - 4 = -1 \][/tex]
4. Perform the subtraction in the denominator (x-coordinates):
[tex]\[ 7 - 10 = -3 \][/tex]
5. Substitute these values back into the slope formula:
[tex]\[ m = \frac{-1}{-3} \][/tex]
6. Simplify the fraction:
[tex]\[ m = \frac{-1}{-3} = \frac{1}{3} \][/tex]
Thus, the slope of the line that passes through the points (10, 4) and (7, 3) is:
[tex]\[ m = \frac{1}{3} \][/tex]
In decimal form, this is approximately:
[tex]\[ 0.3333333333333333 \][/tex]
This is the simplest form of the slope and thus, the solution to the problem.
