To determine the slope and [tex]\(y\)[/tex]-intercept of the linear function passing through the given points, we will follow these steps:
1. Identify the Coordinates:
The given points are [tex]\((-4, 4)\)[/tex] and [tex]\((0, 5)\)[/tex].
2. Calculate the Slope [tex]\(m\)[/tex]:
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:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substitute the given points into the slope formula:
[tex]\[
x_1 = -4, \quad y_1 = 4, \quad x_2 = 0, \quad y_2 = 5
\][/tex]
Thus,
[tex]\[
m = \frac{5 - 4}{0 - (-4)} = \frac{1}{4}
\][/tex]
3. Determine the [tex]\(y\)[/tex]-Intercept:
The [tex]\(y\)[/tex]-intercept is the point where the line crosses the [tex]\(y\)[/tex]-axis. This occurs when [tex]\(x = 0\)[/tex]:
From the given points, we can see that when [tex]\(x = 0\)[/tex], [tex]\(y = 5\)[/tex]. Thus, the [tex]\(y\)[/tex]-intercept is [tex]\((0, 5)\)[/tex].
4. Verify the Answer:
We have calculated the slope to be [tex]\(\frac{1}{4}\)[/tex] and the [tex]\(y\)[/tex]-intercept to be [tex]\((0, 5)\)[/tex].
Therefore, the correct answer is:
A. The slope is [tex]\(\frac{1}{4}\)[/tex]. The [tex]\(y\)[/tex]-intercept is [tex]\((0,5)\)[/tex].
