To determine the slope of a line passing through two points, we 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. In this case, the points given are [tex]\((2, 3)\)[/tex] and [tex]\((0, 11)\)[/tex].
Let's substitute the coordinates of the points into the formula:
1. Identify the coordinates:
[tex]\[ (x_1, y_1) = (2, 3) \][/tex]
[tex]\[ (x_2, y_2) = (0, 11) \][/tex]
2. Substitute these values into the slope formula:
[tex]\[ m = \frac{11 - 3}{0 - 2} \][/tex]
3. Perform the subtraction in the numerator and the denominator:
[tex]\[ m = \frac{8}{-2} \][/tex]
4. Simplify the fraction:
[tex]\[ m = -4 \][/tex]
So, the slope of the line passing through the points (2, 3) and (0, 11) is [tex]\(-4\)[/tex].
