Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−3, 6) and (3, −2)

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Identify the two given points: \((-3, 6)\) and \((3, -2)\).

Calculate the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1, y_1) = (-3, 6)\) and \((x_2, y_2) = (3, -2)\).

Use the point-slope form of a line equation: \(y - y_1 = m(x - x_1)\), substituting \(m\) and one of the points, for example \((-3, 6)\).

Simplify the point-slope form equation to write it explicitly.

Convert the point-slope form equation to slope-intercept form \(y = mx + b\) by solving for \(y\) and simplifying.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Slope of a Line

The slope measures the steepness of a line and is calculated as the change in y-values divided by the change in x-values between two points. For points (x₁, y₁) and (x₂, y₂), slope m = (y₂ - y₁) / (x₂ - x₁). This value is essential for writing the equation of the line.

Point-Slope Form of a Line

Point-slope form expresses a line's equation using a known point (x₁, y₁) and the slope m: y - y₁ = m(x - x₁). It is useful for quickly writing an equation when a point and slope are known, directly relating the line's slope to any point on it.

Slope-Intercept Form of a Line

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. After finding the slope and using a point to solve for b, this form clearly shows the line's slope and where it crosses the y-axis, making it easy to graph.