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 (−2, 6) and is perpendicular to the line whose equation is x = -4.

Verified step by step guidance

1. Identify the slope of the line x = -4. Since this 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 (-2, 6) into the point-slope form: y - 6 = 0(x + 2).
5. Simplify the equation to get the slope-intercept form, y = 6.

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 format allows for easy identification of the line's steepness and where it crosses the y-axis. Understanding this form is crucial for writing equations of lines 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 other line must have a slope of -1/m. In this question, since the line x = -4 is vertical (undefined slope), the line we need to find 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 its slope. In this case, we can use the point (-2, 6) and the slope of 0 to derive the equation in slope-intercept form.