To determine the slope and y-intercept of the linear function that passes through the given points [tex]\((-2, 8)\)[/tex] and [tex]\((0, 6)\)[/tex], we will follow these steps:
### Step 1: Calculate the Slope
The formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging in the given points [tex]\((-2, 8)\)[/tex] and [tex]\((0, 6)\)[/tex]:
[tex]\[
m = \frac{6 - 8}{0 - (-2)} = \frac{6 - 8}{0 + 2} = \frac{-2}{2} = -1
\][/tex]
So, the slope [tex]\( m \)[/tex] is [tex]\(-1\)[/tex].
### Step 2: Calculate the y-Intercept
The y-intercept [tex]\( b \)[/tex] can be found by using the slope-intercept form of the equation of a line: [tex]\( y = mx + b \)[/tex].
We already have the slope [tex]\( m = -1 \)[/tex]. Using the point [tex]\((0, 6)\)[/tex], which lies on the y-axis, we can directly find the y-intercept, since this point represents where the line crosses the y-axis ([tex]\(x = 0\)[/tex]).
When [tex]\( x = 0 \)[/tex],
[tex]\[
y = m \cdot 0 + b \implies y = b
\][/tex]
Given that [tex]\( y = 6 \)[/tex] when [tex]\( x = 0 \)[/tex],
[tex]\[
b = 6
\][/tex]
So, the y-intercept [tex]\( b \)[/tex] is [tex]\( 6 \)[/tex].
### Conclusion
We have found that the slope [tex]\( m \)[/tex] is [tex]\(-1\)[/tex] and the y-intercept [tex]\( b \)[/tex] is [tex]\( 6 \)[/tex].
Therefore, the correct option is:
D. The slope is [tex]\(-1\)[/tex] and the y-intercept is [tex]\((0, 6)\)[/tex].
