1. **State the problem:** We are given two points on line 1: $(-3,5)$ and $(6,8)$. We need to determine which of the given points also lies on this line. 2. **Find the slope of the line:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using the points $(-3,5)$ and $(6,8)$: $$m = \frac{8 - 5}{6 - (-3)} = \frac{3}{9} = \frac{1}{3}$$ 3. **Find the equation of the line:** Using point-slope form: $$y - y_1 = m(x - x_1)$$ Using point $(-3,5)$: $$y - 5 = \frac{1}{3}(x + 3)$$ Simplify: $$y - 5 = \frac{1}{3}x + 1$$ $$y = \frac{1}{3}x + 6$$ 4. **Check each point:** Substitute $x$ into the equation and see if $y$ matches. A) $(0,6)$: $$y = \frac{1}{3}(0) + 6 = 6$$ Matches $y=6$, so point A is on the line. B) $(3,8)$: $$y = \frac{1}{3}(3) + 6 = 1 + 6 = 7$$ Does not match $y=8$, so point B is not on the line. C) $(9,10)$: $$y = \frac{1}{3}(9) + 6 = 3 + 6 = 9$$ Does not match $y=10$, so point C is not on the line. D) $(12,11)$: $$y = \frac{1}{3}(12) + 6 = 4 + 6 = 10$$ Does not match $y=11$, so point D is not on the line. **Final answer:** Only point A $(0,6)$ lies on line 1.