7. the equation of a certain line is $y = 3x + 9$. explain why substituting $y = 0$ into the equation gives the $x$-intercept. name the $x$-intercept of the line.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Algebraic Substitution", "Linear Equations Solving", "x-intercept" ], "new_concepts": [], "current_concepts": [ "Algebraic Substitution", "Linear Equations Solving", "x-intercept" ] } ## Definition of the x-intercept $$ y = 0 $$ ## Solve for the x-intercept $$ \begin{aligned} 0 &= 3x + 9 \ -9 &= 3x \ x &= -3 \end{aligned} $$ ## State the coordinates of the x-intercept $$ (-3, 0) $$ Substituting $y = 0$ into the equation gives the $x$-intercept because the $x$-intercept is the point where the line crosses the $x$-axis, and every point on the $x$-axis has a $y$-coordinate of $0$. The $x$-intercept of the line is $(-3, 0)$ (or $x = -3$). { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "x-intercept" ] }

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Definition of the x-intercept

Solve for the x-intercept

State the coordinates of the x-intercept

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