EQUATION OF HORIZONTAL AND VERTICAL LINES

Problem 1 :

Identify as either a vertical or horizontal line and hence plot the graphs of:

a)  y = 3

Solution :

y = b

So, y = 3 is a horizontal line.

b)  x = 4

Solution :

The given line is parallel to y-axis, so it is vertical line passes through 4.

c)  y = -2

Solution :

The given line is parallel to x-axis, so it is horizontal line.

So, y = -2 is a horizontal line.

d)  x = -6

Solution :

The given line is parallel to y-axis. It is in the form of

x = a

So, x = -6 is a vertical line.

Problem 2 :

Identify as either a vertical or horizontal line:

(i)  a line with zero slope   

(ii)  a line with undefined gradient

Solution :

(i) Horizontal line will have zero slope.

(ii)  The vertical lines only will have undefined slope.

Problem 3 :

Find the equation of:

a) The x-axis 

b) The y-axis

c) A line parallel to the x-axis and two units above it

d)  A line parallel to the y-axis and 3 units to the left of it

Solution :

a) The x-axis equation is y = 0

b) The y-axis equation is x = 0

c) The equation of a straight line parallel to the x-axis at a distance of 2 units above the x-axis is y = 2.

d) The equation of the parallel to y-axis at a distance of 3 units to the left is x = -3.

x + 3 = 0

Problem 4 :

You lose track of how many 2-point baskets and 3-point baskets a team makes in a basketball game. The team misses all the 1-point baskets and still scores 54 points. The equation 2x + 3y = 54 models the total points scored, where x is the number of 2-point baskets made and y is the number of 3-point baskets made.

a. Find and interpret the intercepts.

b. Can the number of 3-point baskets made be odd? Explain your reasoning.

c. Graph the equation. Find two more possible solutions in the context of the problem.

Solution :

2x + 3y = 54

a)

The maximum number of 2 point baskets is 27

The maximum number of 3 point baskets is 18.

b) 3 point basket :

3y = 54 - 2x

y = 54/3 - (2/3)x

y = 18 - (2x/3)

3-point baskets cannot be made.

c)

Problem 5 :

The vertices of a parallelogram are J (− 5, 0), K(1, 4), L(3, 1), and M(− 3, − 3). How can you use slope to determine whether the parallelogram is a rectangle? Is it a rectangle? Justify your answer

Solution :

To check if the parallelogram is a rectangle, the adjacent sides must be perpendicular.

Product of slopes = (2/3)  • (-3/2)

= -1

Since the product of the slopes is equal to -1, the adjacent sides are perpendicular. So, the given vertices will make a rectangle.

Problem 6 :

Graph the equations x = 5, x = 2, y = −2, and y = 1. What enclosed shape do the lines form? Explain your reasoning.

Solution :

x = 5, x = 2, y = −2, and y = 1

Here x = 5 and x = 2 are vertical lines and y = -2, y = 1 are horizontal lines.

Length = 3 units

Width = 3 units.

Since length and width are equal, it must be a square.