To find the slope of the line that passes through the points [tex]\((-4, 5)\)[/tex] and [tex]\((6, 2)\)[/tex], we can use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] represents the coordinates of the first point, [tex]\((-4, 5)\)[/tex], and [tex]\((x_2, y_2)\)[/tex] represents the coordinates of the second point, [tex]\((6, 2)\)[/tex].
Step-by-step solution:
1. Identify the coordinates of the points:
[tex]\[ (x_1, y_1) = (-4, 5) \][/tex]
[tex]\[ (x_2, y_2) = (6, 2) \][/tex]
2. Substitute the coordinates into the slope formula:
[tex]\[ \text{slope} = \frac{2 - 5}{6 - (-4)} \][/tex]
3. Simplify the expressions in the numerator and the denominator:
[tex]\[ \text{slope} = \frac{2 - 5}{6 + 4} \][/tex]
[tex]\[ \text{slope} = \frac{-3}{10} \][/tex]
4. Therefore, the slope of the line passing through the points [tex]\((-4, 5)\)[/tex] and [tex]\((6, 2)\)[/tex] is:
[tex]\[ \text{slope} = -\frac{3}{10} \][/tex]
Hence, the numerical value of the slope is [tex]\(-0.3\)[/tex].
