1. **Problem a:** Determine if the point $(-3,4)$ lies on the line given by the equation $$y + 3x + 2 = 0.$$ 2. Substitute $x = -3$ and $y = 4$ into the line equation: $$4 + 3(-3) + 2 = 4 - 9 + 2 = -3.$$ Since the result is not zero, the point $(-3,4)$ does **not** lie on the line. 3. **Problem b:** Determine if the point $(-4,7)$ lies on the line $$y = -\frac{1}{2}x + 7.$$ 4. Substitute $x = -4$ into the line equation to find $y$: $$y = -\frac{1}{2}(-4) + 7 = 2 + 7 = 9.$$ Since the point has $y=7$ but the line gives $y=9$ at $x=-4$, the point $(-4,7)$ does **not** lie on the line. 5. **Additional expressions:** - Simplify $$7y - 3y = 10 - x + 3$$ $$4y = 13 - x$$ $$y = \frac{13 - x}{4}.$$ - Evaluate $$7 - \frac{2}{5}x + 3 \times \frac{21}{5}$$ (expression incomplete without $x$ value). - Simplify $$y + 3 + \frac{1}{2}y - 4 - y = \frac{1}{2}y - 1.$$ - Point $y(4,17)$ likely means point $(4,17)$ on $y$-axis or function. 6. **Problem c:** Check if point $(4,-3)$ lies on line $$y + 2x = 10.$$ Substitute $x=4$, $y=-3$: $$-3 + 2(4) = -3 + 8 = 5 \neq 10,$$ so point does **not** lie on the line. 7. **Problem d:** Line $$y = -\frac{3}{2}x + 7.$$ Evaluate expressions: $$7x - \frac{2}{3}(6x - 9) = 7x - (4x - 6) = 7x - 4x + 6 = 3x + 6.$$ 8. Expression $$7 + 4 \times \frac{1}{2} + \frac{8}{9} = 7 + 2 + \frac{8}{9} = 9 + \frac{8}{9} = \frac{81}{9} + \frac{8}{9} = \frac{89}{9}.$$ 9. Point $y(43,17)$ likely means point $(43,17)$ on $y$-axis or function. **Summary:** Points $(-3,4)$, $(-4,7)$, and $(4,-3)$ do not lie on their respective lines. Simplifications and evaluations of given expressions are shown above.