Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−2, 6) and is perpendicular to the line whose equation is x = -4.

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Identify the given information: the function ƒ passes through the point \((-2, 6)\) and is perpendicular to the line \(x = -4\).

Recall that the line \(x = -4\) is a vertical line, which means its slope is undefined.

Since the line we want is perpendicular to a vertical line, it must be a horizontal line. Horizontal lines have a slope of 0.

Use the slope-intercept form of a line, which is \(y = m x + b\), where \(m\) is the slope and \(b\) is the y-intercept. Here, \(m = 0\), so the equation simplifies to \(y = b\).

Substitute the point \((-2, 6)\) into the equation \(y = b\) to find \(b\): since \(y = 6\), the equation of the line is \(y = 6\).

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주요 개념

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Slope-Intercept Form

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b is the y-intercept. This form makes it easy to identify the slope and where the line crosses the y-axis, which is essential for graphing and writing linear equations.

Perpendicular Lines

Two lines are perpendicular if their slopes are negative reciprocals of each other. For vertical and horizontal lines, a vertical line has an undefined slope, and a line perpendicular to it is horizontal with a slope of zero. Understanding this helps determine the slope of the required line.

Using a Point to Find the Equation

Given a point on the line and the slope, you can substitute these values into the slope-intercept form to solve for the y-intercept b. This step is crucial to write the complete equation of the line that meets the given conditions.