7 the graph of $7x - 4y = 8$ is shown on the grid.

which points are in the solution set of $7x - 4y

Question

7 the graph of $7x - 4y = 8$ is shown on the grid.

which points are in the solution set of $7x - 4y < 8$?

select two correct answers.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Linear Inequalities", "Ordered Pairs" ], "new_concepts": [ "Two-Variable Inequalities" ], "current_concepts": [ "Linear Inequalities", "Ordered Pairs", "Two-Variable Inequalities" ] } ## Identify the given inequality and points Using the *Linear Inequalities* and *Ordered Pairs* knowledge points $$ \begin{aligned} &\text{Inequality: } 7x - 4y < 8\ &P_1 = (-4, 1)\ &P_2 = (-1, 3)\ &P_3 = (3, -4)\ &P_4 = (5, 3) \end{aligned} $$ ## Test the first point Using the *Ordered Pairs* knowledge point $$ \begin{aligned} &\text{Substitute } (-4, 1):\ &7(-4) - 4(1) = -28 - 4 = -32\ &-32 < 8 \quad (\text{True}) \end{aligned} $$ ## Test the second point Using the *Ordered Pairs* knowledge point $$ \begin{aligned} &\text{Substitute } (-1, 3):\ &7(-1) - 4(3) = -7 - 12 = -19\ &-19 < 8 \quad (\text{True}) \end{aligned} $$ ## Test the third point Using the *Ordered Pairs* knowledge point $$ \begin{aligned} &\text{Substitute } (3, -4):\ &7(3) - 4(-4) = 21 + 16 = 37\ &37 ot< 8 \quad (\text{False}) \end{aligned} $$ ## Test the fourth point Using the *Ordered Pairs* knowledge point $$ \begin{aligned} &\text{Substitute } (5, 3):\ &7(5) - 4(3) = 35 - 12 = 23\ &23 ot< 8 \quad (\text{False}) \end{aligned} $$

(A) $(-4, 1)$

(B) $(-1, 3)$

(C) $(3, -4)$

(D) $(5, 3)$

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QUESTION IMAGE

Question

Explanation:

Identify the given inequality and points

Test the first point

Test the second point

Test the third point

Test the fourth point

Answer: