To determine the slope of the line represented by the points in the table, we start by using the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], which is given by:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Using the points [tex]\((-2, -0.35)\)[/tex] and [tex]\((-1, -0.3)\)[/tex] from the table, let's calculate the slope:
1. Calculate the change in [tex]\(y\)[/tex] values, [tex]\(\Delta y\)[/tex]:
[tex]\[ \Delta y = y_2 - y_1 = -0.3 - (-0.35) \][/tex]
[tex]\[ \Delta y = -0.3 + 0.35 = 0.05 \][/tex]
2. Calculate the change in [tex]\(x\)[/tex] values, [tex]\(\Delta x\)[/tex]:
[tex]\[ \Delta x = x_2 - x_1 = -1 - (-2) \][/tex]
[tex]\[ \Delta x = -1 + 2 = 1 \][/tex]
3. Now, we can find the slope:
[tex]\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{0.05}{1} = 0.05 \][/tex]
Thus, the slope of the line represented by the points in the table is [tex]\(0.05\)[/tex].
The correct answer is [tex]\(0.05\)[/tex].
