Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-8,4), undefined slope

검증된 단계별 안내

Identify the key information: the line passes through the point (-8, 4) and has an undefined slope. An undefined slope means the line is vertical.

Recall that a vertical line has an equation of the form \(x = a\), where \(a\) is the x-coordinate of every point on the line.

Since the line passes through (-8, 4), the x-coordinate for all points on the line is -8.

Write the equation of the line as \(x = -8\).

Note that this equation is already in standard form because it cannot be expressed in slope-intercept form (which requires a defined slope).

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주요 개념

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Undefined Slope

An undefined slope occurs when a line is vertical, meaning it goes straight up and down. This happens because the change in x (horizontal change) is zero, making the slope formula (change in y divided by change in x) undefined. Such lines have equations of the form x = a constant.

Equation of a Vertical Line

A vertical line passing through a point (x, y) has an equation x = k, where k is the x-coordinate of the point. Since the slope is undefined, the line does not have a slope-intercept form (y = mx + b). The equation simply states that x is constant for all points on the line.

Standard Form of a Linear Equation

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A ≥ 0. For vertical lines, this form is useful because it can represent x = k as 1·x + 0·y = k. This form is often preferred for clarity and consistency in expressing linear equations.