Question
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\( 1 \leftarrow \) Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Slope \( =-9 \), passing through \( (-8,-8) \) Type the point-slope form of the line. (Simplify your answer. Use integers or fractions for any numbers in the equation.)

Ask by Cook Turnbull. in the United States
Feb 26,2025

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Answer

Point-slope form: \( y + 8 = -9(x + 8) \)

Solution

Point-slope form: y + 8 = -9(x + 8) To explain: 1. Start with the point-slope form equation: y - y₁ = m(x - x₁) 2. Substitute m = -9, x₁ = -8, and y₁ = -8:   y - (-8) = -9(x - (-8))   y + 8 = -9(x + 8)

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To write the equation in point-slope form, you can use the formula \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point through which the line passes. Here, \( m = -9 \) and the point is \( (-8, -8) \). Substituting, we get: \[ y - (-8) = -9(x - (-8)) \] Simplifying that gives: \[ y + 8 = -9(x + 8) \] Now, let's convert it to slope-intercept form \( y = mx + b \). Start with the above equation: 1. Distribute: \( y + 8 = -9x - 72 \) 2. Isolate \( y \): \( y = -9x - 80 \) So, the point-slope form is \( y + 8 = -9(x + 8) \) and the slope-intercept form is \( y = -9x - 80 \).

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