writing linear equations (given two points)

to write a linear equation that passes through two points $(x_1, y_1)$ and $(x_2, y_2)$, use the slope formula followed by the point-slope formula:

slope formula:
\m = \frac{y_2 - y_1}{x_2 - x_1}\

point-slope formula:
\y - y_1 = m(x - x_1)\

directions: write the equation of the line that passes through the given two points. write all final answers in slope-intercept form.

1. $(-3, 7)$ and $(1, -1)$
2. $(-6, -7)$ and $(3, -4)$
3. $(2, -1)$ and $(4, -6)$
4. $(1, 6)$ and $(2, 5)$
5. $(-8, 1)$ and $(0, -5)$
6. $(-3, -8)$ and $(2, 7)$

Question

writing linear equations (given two points)

to write a linear equation that passes through two points $(x_1, y_1)$ and $(x_2, y_2)$, use the slope formula followed by the point-slope formula:

slope formula:
\m = \frac{y_2 - y_1}{x_2 - x_1}\

point-slope formula:
\y - y_1 = m(x - x_1)\

directions: write the equation of the line that passes through the given two points. write all final answers in slope-intercept form.

1. $(-3, 7)$ and $(1, -1)$
2. $(-6, -7)$ and $(3, -4)$
3. $(2, -1)$ and $(4, -6)$
4. $(1, 6)$ and $(2, 5)$
5. $(-8, 1)$ and $(0, -5)$
6. $(-3, -8)$ and $(2, 7)$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Slope Formula", "Point-Slope Form", "Slope-Intercept Form" ], "current_concepts": [ "Slope Formula", "Point-Slope Form", "Slope-Intercept Form" ] } ## Calculate slopes for both questions $$ \begin{aligned} &\text{For Question 5: } (-8, 1) \text{ and } (0, -5)\ &m_5 = \frac{-5 - 1}{0 - (-8)} = \frac{-6}{8} = -\frac{3}{4}\ \ &\text{For Question 6: } (-3, -8) \text{ and } (2, 7)\ &m_6 = \frac{7 - (-8)}{2 - (-3)} = \frac{15}{5} = 3 \end{aligned} $$ ## Apply point-slope form and solve for y $$ \begin{aligned} &\text{For Question 5 using } (0, -5):\ &y - (-5) = -\frac{3}{4}(x - 0)\ &y + 5 = -\frac{3}{4}x\ &y = -\frac{3}{4}x - 5\ \ &\text{For Question 6 using } (2, 7):\ &y - 7 = 3(x - 2)\ &y - 7 = 3x - 6\ &y = 3x + 1 \end{aligned} $$ ## Question 5 $y = -\frac{3}{4}x - 5$ ## Question 6 $y = 3x + 1$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate slopes for both questions

Apply point-slope form and solve for y

Answer:

Question 5

Question 6