a line passes through the point $(8, -9)$ and has a slope of $-\frac{5}{4}$.

write an equation in slope-intercept form for this line.

Question

a line passes through the point $(8, -9)$ and has a slope of $-\frac{5}{4}$.

write an equation in slope-intercept form for this line.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope-Intercept Form", "Point-Slope Equation" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Point-Slope Equation" ] } ## Use point-slope form to write the initial equation $$ \begin{aligned} &(x_1, y_1) = (8, -9),\quad m = -\frac{5}{4}\ &y - y_1 = m(x - x_1)\ &y - (-9) = -\frac{5}{4}(x - 8) \end{aligned} $$ ## Simplify and solve for y to get slope-intercept form $$ \begin{aligned} &y + 9 = -\frac{5}{4}x + 10\ &y = -\frac{5}{4}x + 1 \end{aligned} $$ A line passes through the point $(8, -9)$ and has a slope of $-\frac{5}{4}$. Write an equation in slope-intercept form for this line. $y = -\frac{5}{4}x + 1$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Slope-Intercept Form" ] }

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QUESTION IMAGE

Question

Explanation:

Use point-slope form to write the initial equation

Simplify and solve for y to get slope-intercept form

Answer: