In Exercises 19–24, write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−1, 5) and is perpendicular to the line whose equation is x = 6.

Verified step by step guidance

1. Identify the slope of the line x = 6. Since x = 6 is a vertical line, its slope is undefined.
2. A line perpendicular to a vertical line is a horizontal line, which has a slope of 0.
3. Use the point-slope form of a line equation: y - y_1 = m(x - x_1), where m is the slope and (x_1, y_1) is a point on the line.
4. Substitute the slope m = 0 and the point (-1, 5) into the point-slope form: y - 5 = 0(x + 1).
5. Simplify the equation to get the slope-intercept form y = mx + b, which results in y = 5.

Key Concepts

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope of the line and b is the y-intercept. This form is useful for quickly identifying the slope and y-intercept, allowing for easy graphing of the line. Understanding this format is essential for writing the equation of a line based on given conditions.

Perpendicular Lines

Two lines are perpendicular if the product of their slopes is -1. This means that if one line has a slope of m, the slope of the line perpendicular to it will be -1/m. In this case, since the line x = 6 is vertical (undefined slope), the perpendicular line will be horizontal, having a slope of 0.

Point-Slope Form

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is particularly useful when you know a point through which the line passes and the slope of the line. It can be converted to slope-intercept form to find the equation of the line.