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Chapter 2: Problem 19

Write an equation in slope-intercept form of a linear function \(f\) whose graph satisfies the given conditions. The graph of \(f\) passes through \((-1,5)\) and is perpendicular to the line whose equation is \(x=6\)

Short Answer

Expert verified
The equation of the line in slope-intercept form is \(y = 5\).

Step by step solution

01

Understand the Line

The line that the function \(f\) is perpendicular to is \(x=6\). Recall that this is a vertical line. The line that is perpendicular to a vertical line is horizontal. The slope of any horizontal line is 0. So the slope (\(m\)) for our line is 0.
02

Determine the Y-intercept

Given that the line of function \(f\) passes through the point (-1,5), since this is a horizontal line, it would pass through any point where y=5. Hence, the y-intercept (\(c\)) of our line would be 5.
03

Write the Equation

Substitute \(m\) and \(c\) into the slope-intercept form \(y = mx + c\) that gives the equation of the line as \(y = 0x + 5\). We can simplify this to \(y = 5\).

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