Question

Find the equation of the lines for which $\tan \theta = \dfrac{1}{2}$, where $\theta $ is the angle of inclination of the line and x – intercept is 4.

Answer 1

Hint: In this question, we have one point that is x which intercept at (4, 0) and a slope to get the equation of a line. We will put these values in the formula of the equation of a line.
Equation of a line $y - {y_1} = m(x - {x_1})$.

Complete step-by-step answer:
Given,
$\tan \theta = \dfrac{1}{2}$
Slope of a line (m) = $\tan \theta $$ = \dfrac{1}{2}$
x – intercept at (4, 0)
We know that equation of a line passing through a point and having a slope is given as:
$y - {y_1} = m(x - {x_1})$
Here, we know that m is the slope of a line.
$y - 0 = \dfrac{1}{2}(x - 4)$
$\dfrac{{y - 0}}{{x - 4}} = \dfrac{1}{2}$
Cross multiplying the number, we have;
$\begin{gathered}
  2y = x - 4 \\
   \Rightarrow x - 2y - 4 = 0 \\
\end{gathered} $
$x – 2y – 4$ is the required equation of the line.

Note: The intercept of a line is the point at which it crosses either the x or y axis. If we do not specify which one, then y – axis is assumed. The slope of a line in the plane containing the x – axis and y – axis is generally represented by the letter m, and is defined as the change in the y – coordinate divided by the corresponding change in the x – coordinate between two distinct points on the line. If y is a linear function of x, then the coefficient of x is the slope of the line created by plotting the function. Therefore, if the equation of the line is given in the form of y = mx + b then m is the slope. This form of a line’s equation is called the slope-intercept form.