Question

Write the equation of each of the following lines:

1. The x-axis and the y-axis.
2. The line passing through the origin and the point (-3, 5).
3. The line passing through the point (-3, 4) and parallel to X-axis.

Answer 1

1. The required equation of x-axis is y = 0 and y-axis is x = 0.

2. Let P ≡ (0,0) ≡ (x₁, y₁) and Q ≡ (-3,5) ≡ (x₂,y₂)

The required equation is

${\displaystyle \frac{x-x_1}{x_1-x_2}=\frac{\text{y}-{\text{y}}_1}{{\text{y}}_1-{\text{y}}_2}}$

${\displaystyle \frac{x-0}{0+3}=\frac{\text{y}-0}{0-5}}$

${\displaystyle \frac{x}{3}=\frac{\text{y}}{-5}}$

${\displaystyle 5x+3\text{y}=0}$

 

3. The equation of x-axis line is y = 0

Slope of the line = 0

Required line is parallel to X-axis we know that parallel lines have equal slopes.

Slope of the required line = m= 0 and point (-3, 4) is on the line.

By point slope form of equation,

y - y1 = m(x - x1)

y - 4 = 0(x - (-3))

y = 4 is the required equation.