Question

Investigate the slopes of vertical and horizontal lines by answering the following

(a) The point (4,6) is on a vertical line. Name another point on that line.


(b)The formula for the slope of the line given two points on that line is m y_2 - y_1 / x_2 - x_1 Evaluate the denominator
of the slope formula for the two points named in part (a).

(C) The point (4, 6) is on a horizontal line. Name another point on that line.

(d) The formula for the slope of the line given two points on that line is m= y_2 - y_1 / x_2 - x_1 - Evaluate numerator of the stope formula for the two points named in part (C).

Answer 1

On a vertical line, the x-coordinate remains the same for any point, while on a horizontal line, the y-coordinate remains the same. The denominator of the slope formula for the vertical line is either -4 or 4, and the numerator for the horizontal line is 0.

Step-by-step explanation:

(a) Since (4,6) is on a vertical line, another point on that line could be (4,2) or (4,10), as the x-coordinate remains the same for any point on a vertical line.

(b) To find the slope of the line, we need to evaluate the denominator of the slope formula for the two points named in part (a). Using the formula: m = (y2 - y1) / (x2 - x1), the denominator would be (2 - 6) = -4 or (10 - 6) = 4.

(c) Since (4,6) is on a horizontal line, another point on that line could be (2,6) or (6,6), as the y-coordinate remains the same for any point on a horizontal line.

(d) To find the slope of the line, we need to evaluate the numerator of the slope formula for the two points named in part (c). Using the formula: m = (y2 - y1) / (x2 - x1), the numerator would be (6 - 6) = 0, as the y-coordinates are the same.