A linear function has an x-intercept of `sqrt(3)` and a y-intercept of `sqrt(5)`. The graph of the function has a slope of

Options

A. `-1.29`
B. `-0.77`
C. `1.29`
D. `2.24`

Explanation

To find the slope of the linear function given its x-intercept and y-intercept, we can follow these steps:

### Step 1: Understand the intercepts
The x-intercept is given as \( \sqrt{3} \) and the y-intercept is given as \( \sqrt{5} \). This means the line crosses the x-axis at \( (\sqrt{3}, 0) \) and the y-axis at \( (0, \sqrt{5}) \).

### Step 2: Use the intercept form of the line
The intercept form of a line is given by the equation:
\[ \frac{x}{a} + \frac{y}{b} = 1 \]
where \( a \) is the x-intercept and \( b \) is the y-intercept. Substituting the values:
\[ \frac{x}{\sqrt{3}} + \frac{y}{\sqrt{5}} = 1 \]

### Step 3: Rearranging the equation
To find the slope, we need to express the equation in the slope-intercept form \( y = mx + c \). Rearranging the equation:
\[ \frac{y}{\sqrt{5}} = -\frac{x}{\sqrt{3}} + 1 \]
Multiplying through by \( \sqrt{5} \):
\[ y = -\frac{\sqrt{5}}{\sqrt{3}} x + \sqrt{5} \]

### Step 4: Identify the slope
From the equation \( y = mx + c \), we can see that the slope \( m \) is:
\[ m = -\frac{\sqrt{5}}{\sqrt{3}} \]

### Step 5: Calculate the numerical value of the slope
To find the numerical value of the slope, we can calculate:
\[ m = -\frac{\sqrt{5}}{\sqrt{3}} \approx -1.29 \]

### Final Answer
Thus, the slope of the linear function is approximately:
\[ m \approx -1.29 \]

---