1. **State the problem:** We have a linear function graphed as a straight line passing through points including (-2,7), (0,5), and (6,1). We need to find outputs for given inputs, inputs for given outputs, the equation of the function, and an input-output pair. 2. **Find the equation of the line:** The line passes through (-2,7) and (0,5). The slope formula is $$m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-7}{0-(-2)}=\frac{-2}{2}=-1.$$ So the slope is $-1$. 3. **Use point-slope form:** Using point (0,5), the equation is $$y - 5 = -1(x - 0)$$ which simplifies to $$y = -x + 5.$$ This matches the points given. 4. **Answer A: Output when input is 6:** Substitute $x=6$ into $y=-x+5$: $$y = -(6) + 5 = -6 + 5 = -1.$$ So output is $-1$. 5. **Answer B: Input when output is 6:** Set $y=6$ and solve for $x$: $$6 = -x + 5$$ $$6 - 5 = -x$$ $$1 = -x$$ $$x = -1.$$ So input is $-1$. 6. **Answer C: Output when input is 2:** Substitute $x=2$: $$y = -2 + 5 = 3.$$ Output is $3$. 7. **Answer D: Equation representing the function:** The equation is $$y = -x + 5.$$ 8. **Answer E: An input-output pair:** For example, $(0,5)$ is on the line. Final answers: A: $-1$ B: $-1$ C: $3$ D: $y = -x + 5$ E: $(0,5)$