In the xy-coordinate system, do any points on line k lie in

tejal777, below are my notes and tips about the slope of a line and the quadrants of intersect of a line depending on a slope. Hope you find them useful:

The slope is defined as “rise over run,” or the distance the line runs vertically divided by the distance the line runs horizontally. The slope of any given line is constant over the length of that line. Given any two points on the line, take the difference between the y (or vertical) coordinates and divide that by the difference between the x (or horizontal) coordinates.

Equation of a line y=mx+b: slope m, b Y intersect.
OR
Equation of a line ay+bx+c=0: slope -b/a, -c/a Y intersect.

1. If the slope of line is negative, line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, line intersects the quadrant I too, if negative quadrant III.

2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV.

3. Every line (but the one crosses origin OR parallel to X or Y axis OR X and Y axis themselves) crosses three quadrants. Only the line which crosses origin (0,0) OR is parallel of either of axis crosses two quadrants.

4. If a line is horizontal the line has slope 0, is parallel to X-axis and crosses quadrant I and II, if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative. Equation of such line is y=b, where b is y intersect.

5. If a line is vertical, the slope is not defined, line is parallel to Y-axis and crosses quadrant I and IV, if the X intersect is positive and quadrant II and III, if the X intersect is negative. Equation of such line is x=a, where a is x-intercept.

6. For the line crosses the two points (x1,y1) and (x2,y2), slope m=(y1-y2)/(x1-x2)

7. If the slope is 1 the angle formed by the line by X and Y axis is 45 degrees.

8. If the slope of a line is m, the slope of a line perpendicular to it is its negative reciprocal, -1/m. Hence two lines are perpendicular if and only the product of their slopes is -1.

9. Parallel lines have same slope.

10. Given a point and slope, equation of the line can be found. The equation of a straight line that passes through a point (x1, y1) with a slope m is: y - y1 = m(x - x1)