Question

Draw the graph of the following line:

3y + 5 = 0

Answer 1

The graph of the equation 3y + 5 = 0 is a horizontal line passing through the `y = - 5/3` (approximately –1.67).

1. Isolate the variable y

 We first solve for y to put it in a recognizable form.

3y + 5 = 0

Subtract 5 from both sides:

3y = –5

Divide by 3:

`y = -5/3`

2. Identify the line characteristics

Because the equation only contains the variable y and no x, the value of y remains constant regardless of what x is.

Slope (m): The slope is 0 because there is no “rise” as x changes.

Y-intercept: The line crosses the y-axis at the point `(0, -5/3)`.

Orientation: The line is perfectly horizontal and parallel to the x-axis.

3. Plot the points

To draw this simply move down the y-axis to roughly –1.67 and draw a straight line left to right. Every point on this line, such as (–2, –1.67), (0, –1.67) or (3, –1.67), satisfies the original equation.