QuestionAugust 24, 2025

1. Select all the points that are on the graph of the equation 4y-6x=12 A (-4,-3) B (-1,1.5) C (0,-2) D (0,3) E (3,-4) F (6,4)

1. Select all the points that are on the graph of the equation 4y-6x=12 A (-4,-3) B (-1,1.5) C (0,-2) D (0,3) E (3,-4) F (6,4)
1. Select all the points that are on the graph of the equation 4y-6x=12 A (-4,-3) B (-1,1.5) C (0,-2) D (0,3) E (3,-4) F (6,4)

Solution
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Answer

A (-4,-3), B (-1,1.5), D (0,3) Explanation 1. Rearrange the Equation Solve for y: 4y = 6x + 12 \Rightarrow y = \frac{3}{2}x + 3. 2. Check Each Point Substitute each point into y = \frac{3}{2}x + 3 to verify if it satisfies the equation. - **Point A**: (-4, -3) y = \frac{3}{2}(-4) + 3 = -6 + 3 = -3. True. - **Point B**: (-1, 1.5) y = \frac{3}{2}(-1) + 3 = -1.5 + 3 = 1.5. True. - **Point C**: (0, -2) y = \frac{3}{2}(0) + 3 = 3 \neq -2. False. - **Point D**: (0, 3) y = \frac{3}{2}(0) + 3 = 3. True. - **Point E**: (3, -4) y = \frac{3}{2}(3) + 3 = 4.5 + 3 = 7.5 \neq -4. False. - **Point F**: (6, 4) y = \frac{3}{2}(6) + 3 = 9 + 3 = 12 \neq 4. False.

Explanation

1. Rearrange the Equation<br /> Solve for $y$: $4y = 6x + 12 \Rightarrow y = \frac{3}{2}x + 3$.<br /><br />2. Check Each Point<br /> Substitute each point into $y = \frac{3}{2}x + 3$ to verify if it satisfies the equation.<br /><br />- **Point A**: $(-4, -3)$ <br /> $y = \frac{3}{2}(-4) + 3 = -6 + 3 = -3$. True.<br /> <br />- **Point B**: $(-1, 1.5)$ <br /> $y = \frac{3}{2}(-1) + 3 = -1.5 + 3 = 1.5$. True.<br /> <br />- **Point C**: $(0, -2)$ <br /> $y = \frac{3}{2}(0) + 3 = 3 \neq -2$. False.<br /> <br />- **Point D**: $(0, 3)$ <br /> $y = \frac{3}{2}(0) + 3 = 3$. True.<br /> <br />- **Point E**: $(3, -4)$ <br /> $y = \frac{3}{2}(3) + 3 = 4.5 + 3 = 7.5 \neq -4$. False.<br /> <br />- **Point F**: $(6, 4)$ <br /> $y = \frac{3}{2}(6) + 3 = 9 + 3 = 12 \neq 4$. False.
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