To solve this problem, we need to determine the slope and the y-intercept of the linear function passing through the given points [tex]\((-4, 4)\)[/tex] and [tex]\((0, 5)\)[/tex].
Let's walk through the steps systematically:
### Step 1: Calculate the Slope
The slope [tex]\(m\)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Given points are:
[tex]\[
(x_1, y_1) = (-4, 4) \quad \text{and} \quad (x_2, y_2) = (0, 5)
\][/tex]
Substitute these values into the slope formula:
[tex]\[
m = \frac{5 - 4}{0 - (-4)} = \frac{1}{4}
\][/tex]
So, the slope [tex]\(m\)[/tex] is [tex]\(\frac{1}{4}\)[/tex].
### Step 2: Determine the y-Intercept
The y-intercept of a line is the point where the line crosses the y-axis. This occurs when [tex]\(x = 0\)[/tex]. From the given points, we can directly observe that when [tex]\(x = 0\)[/tex], [tex]\(y = 5\)[/tex].
Therefore, the y-intercept is [tex]\((0, 5)\)[/tex].
### Conclusion
With the calculated slope and identified y-intercept, we can conclude:
- The slope of the function is [tex]\(\frac{1}{4}\)[/tex].
- The y-intercept of the function is [tex]\((0, 5)\)[/tex].
Thus, the correct answer is:
A. The slope is [tex]\(\frac{1}{4}\)[/tex]. The y-intercept is [tex]\((0,5)\)[/tex].
