1. **State the problem:** We are given the linear function $f(x) = -\frac{3}{5}x + 2$ and want to understand its properties. 2. **Formula and rules:** This is a linear function of the form $f(x) = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, the slope $m = -\frac{3}{5}$ and the y-intercept $b = 2$. 4. **Interpret slope:** The slope $-\frac{3}{5}$ means for every increase of 5 units in $x$, $f(x)$ decreases by 3 units. 5. **Find x-intercept:** Set $f(x) = 0$ to find the x-intercept: $$ 0 = -\frac{3}{5}x + 2 $$ Rearranging: $$ \frac{3}{5}x = 2 $$ Multiply both sides by 5: $$ 3x = 10 $$ Divide both sides by 3: $$ x = \frac{10}{3} $$ 6. **Summary:** The function crosses the y-axis at $(0, 2)$ and the x-axis at $\left(\frac{10}{3}, 0\right)$. 7. **Graph features:** The function is decreasing due to the negative slope. **Final answer:** The x-intercept is $\frac{10}{3}$ and the y-intercept is 2.