A solution to problem 6.18 along with some code to test if the methods are written correctly.

First, a class containing main.

public class Main {
    public static void main(String[] meow) {
        Line a = new Line(-2, 1.5);
        Line b = new Line(0, 1, 2, 2);
        Line c = new Line(1, 3, -2);
        Line d = new Line(4);
        Line e = new Line(-2, 5);
        System.out.println(b.getSlope() + " " + b.getIntercept());
        System.out.println(a.isParallel(b));   // false
        System.out.println(a.isParallel(c));   // true
        System.out.println(a.isPerpendicular(b));  // m1=-2, m2=.5
        System.out.println(a.equals(b));       // false
        System.out.println(e.equals(c));       // true
    }
}
Now, the Line class.

public class Line {
    private double m;    // slope
    private double b;    // y-intercept
    private boolean isVertical = false;
    private double k;
    
    // Assume that for all constructors except the
    // single input constructor (i.e., x = k), there
    // will be no division by zero (i.e., x1 != x2).
    
    // Given m, b
    public Line(double m, double b) {
        this.m = m;
        this.b = b;
    }
    
    // Given a point and slope, find the y-intercept
    public Line(double x1, double y1, double m) {
        this.m = m;
        b = y1 - (m*x1);
    }
    
    // Given two points, must find slope and y-intercept
    public Line(double x1, double y1, double x2, double y2) {
        m = (y2-y1)/(x2-x1);
        b = y1 - (m*x1);
    }
    
    // x = k
    public Line(double k) {
        isVertical = true;
        this.k = k;
    }
    
    public double getSlope() { return m; }
    public double getIntercept() { return b; }
    
    public boolean isParallel(Line l2) {
        if (isVertical && l2.isVertical) return true;
        else if (isVertical || l2.isVertical) return false;
        else return (m == l2.m);
    }
    
    public boolean isPerpendicular(Line l2) {
        if (isVertical && !(l2.isVertical)) return (l2.m == 0);
        else if (!(isVertical) && l2.isVertical) return (m == 0);
        else if (!(isVertical) && !(l2.isVertical))
            return (m * l2.m == -1);
        else return false;
    }
    
    public boolean equals(Line l2) {
        return ((isVertical && l2.isVertical && k == l2.k) ||
                (!(isVertical) && !(l2.isVertical) && m == l2.m && b == l2.b));
    }
}