To find the slope of the line that passes through a point and has a given y-intercept, we'll use the slope formula which is given by:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
In this case, we are given the point [tex]\((x_1, y_1) = (-6.2, 1.1)\)[/tex] and the y-intercept [tex]\((x_2, y_2) = (0, -2)\)[/tex]. The x-coordinate of a y-intercept is always 0 because it is the point where the line crosses the y-axis.
Now let's calculate the slope.
Substitute the values into the slope formula:
[tex]\[ \text{slope} = \frac{-2 - 1.1}{0 - (-6.2)} \][/tex]
[tex]\[ \text{slope} = \frac{-2 - 1.1}{0 + 6.2} \][/tex]
[tex]\[ \text{slope} = \frac{-3.1}{6.2} \][/tex]
Now, simplify the fraction:
[tex]\[ \text{slope} = -\frac{3.1}{6.2} \][/tex]
[tex]\[ \text{slope} = -0.5 \][/tex]
So the slope of the line is [tex]\(-0.5\)[/tex], which can be rounded to three decimal places as [tex]\(-0.500\)[/tex].
