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Question
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.
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.
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