1. **State the problem:** We have two linear functions, Function A and Function B. We need to compare their x-intercepts and y-intercepts. 2. **Find the equation of Function A:** Given points for Function A are $(-8,0)$, $(-5,5)$, and $(0,16)$. Since it's linear, use the slope formula between two points: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 0}{-5 - (-8)} = \frac{5}{3}$$ 3. Use point-slope form with point $(0,16)$ (y-intercept): $$y = mx + b$$ $$16 = \frac{5}{3} \times 0 + b \Rightarrow b = 16$$ So, Function A's equation is: $$y = \frac{5}{3}x + 16$$ 4. **Find x-intercept of Function A:** Set $y=0$: $$0 = \frac{5}{3}x + 16$$ $$\frac{5}{3}x = -16$$ $$x = -16 \times \frac{3}{5} = -\frac{48}{5} = -9.6$$ 5. **Find y-intercept of Function A:** From step 3, $y$-intercept is $16$. 6. **Find intercepts of Function B:** Given equation: $$3y = 8x + 48$$ Rewrite in slope-intercept form: $$y = \frac{8}{3}x + 16$$ - **x-intercept:** Set $y=0$: $$0 = \frac{8}{3}x + 16$$ $$\frac{8}{3}x = -16$$ $$x = -16 \times \frac{3}{8} = -6$$ - **y-intercept:** When $x=0$, $$y = 16$$ 7. **Compare intercepts:** - x-intercept of Function A is $-9.6$, Function B is $-6$. Since $-9.6 < -6$, Function A's x-intercept is \textbf{less than} Function B's. - y-intercept of both functions is $16$, so they are \textbf{equal}. **Final answers:** - The x-intercept of Function A is **less than** the x-intercept of Function B. - The y-intercept of Function A is **equal to** the y-intercept of Function B.