To determine the slope of a line passing through the points [tex]\((-7, 5)\)[/tex] and [tex]\((-3, 4)\)[/tex], we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's label our coordinates:
- [tex]\((x_1, y_1) = (-7, 5)\)[/tex]
- [tex]\((x_2, y_2) = (-3, 4)\)[/tex]
Now, we find the change in [tex]\(y\)[/tex] ([tex]\(y_2 - y_1\)[/tex]) and the change in [tex]\(x\)[/tex] ([tex]\(x_2 - x_1\)[/tex]):
1. Calculate [tex]\(y_2 - y_1\)[/tex]:
[tex]\[ y_2 - y_1 = 4 - 5 = -1 \][/tex]
2. Calculate [tex]\(x_2 - x_1\)[/tex]:
[tex]\[ x_2 - x_1 = -3 - (-7) = -3 + 7 = 4 \][/tex]
Next, we use these changes to determine the slope:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1}{4} \][/tex]
So, the slope of the line passing through the points [tex]\((-7, 5)\)[/tex] and [tex]\((-3, 4)\)[/tex] is:
[tex]\[ \text{slope} = -0.25 \][/tex]
