The inclination of the line x-y+3=0 with the positive direction of x-axis is*
Answers
Answer:
(A) is the correct answer. The equation of the line x – y + 3 = 0 can be rewritten as y = x + 3 ⇒ m = tan θ = 1 and hence θ = 45°.
Given:
A straight line with equation x - y +3 = 0.
To Find:
The Inclination of the line with the positive x-axis.
Solution:
The above problem can be solved by using the properties of 2-D straight lines.
1. The equation of the given line is x - y +3 =0.
2. Consider an equation of the straight line as ax+by+c=0 Then, According to the properties of straight lines, the slope of the line with the positive x-axis is given by the formula,
Slope of ax+by+c with +ve x-axis = -(co-efficient of y)/(co-efficient of x).
=> Slope(m) = -(y co-effiecient)/(x co-efficient).
3. Slope is also denoted by the symbol m.
4. Comparing the given with the above form, we can conclude the following:
- value of a is +1 (co-efficient of x).
- value of b is -1 ( co-efficient of y).
5. Substituting the obtained values in the formula, we get,
slope ( m ) = -(-1)/(1),
=> slope (m) = 1.
6. According to the properties of straight lines slope, slope (m) = tan(α),
where α is the angle made by the line with the +ve x-axis.
7. Therefore, From the above property we can Obtain the following relation i.e, m = tanα = 1.
=> tanα = 1,
=> α = 45°.
Therefore, the angle made by the line x-y+3=0 with the positive direction of the x-axis is 45°.