# Write the equation of each of the following lines: The x-axis and the y-axis. The line passing through the origin and the point (-3, 5). The line passing through the point (-3, 4) and parallel to X-axis. - Geometry

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.

#### Solution

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

(x-x_1)/(x_1-x_2)=("y"-"y"_1)/("y"_1-"y"_2)

(x-0)/(0+3)=("y"-0)/(0-5)

x/3="y"/-5

5x + 3"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.

Concept: General Equation of a Line
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