writing the standard form of a line

write the equation of the line that passes through the points $(8, -1)$ and $(2, -5)$ in standard form, given that the point-slope form is $y + 1 = \frac{2}{3}(x - 8)$.

$\quadx + \quady = \quad$

Question

writing the standard form of a line

write the equation of the line that passes through the points $(8, -1)$ and $(2, -5)$ in standard form, given that the point-slope form is $y + 1 = \frac{2}{3}(x - 8)$.

$\quadx + \quady = \quad$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Point-Slope Form", "Distributive Property", "Algebraic Rearrangement" ], "new_concepts": [ "Standard Form of a Line" ], "current_concepts": [ "Point-Slope Form", "Distributive Property", "Algebraic Rearrangement", "Standard Form of a Line" ] } ## Eliminate the fraction Using the **Point-Slope Form** and **Algebraic Rearrangement** knowledge points $$ \begin{aligned} y + 1 &= \frac{2}{3}(x - 8) \ 3(y + 1) &= 2(x - 8) \end{aligned} $$ ## Expand both sides Using the **Distributive Property** knowledge point $$ \begin{aligned} 3y + 3 &= 2x - 16 \end{aligned} $$ ## Rearrange to standard form Using the **Algebraic Rearrangement** knowledge point $$ \begin{aligned} -2x + 3y + 3 &= -16 \ -2x + 3y &= -19 \ 2x - 3y &= 19 \ 2x + (-3)y &= 19 \end{aligned} $$ Write the equation of the line that passes through the points $(8, -1)$ and $(2, -5)$ in standard form, given that the point-slope form is $y + 1 = \frac{2}{3}(x - 8)$. 2$x +$ -3$y =$ 19 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Standard Form of a Line" ] }

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QUESTION IMAGE

Question

Explanation:

Eliminate the fraction

Expand both sides

Rearrange to standard form

Answer: