Find the equation of a line that makes an intercept of $-3$ on the $y$-axis and makes an angle of ${\tan ^{ - 1}}\frac{3}{5}$ with the $x$-axis.

The equations of the lines which cut off an intercept of $-1$ from the $y$-axis and are equally inclined to the axes are

In the figure,a time-distance graph of a linear motion is given. Two positions of time and distance are recorded as: when $T = 0, D = 2$ and when $T = 3, D = 8$. Using the concept of slope,find the law of motion,i.e.,how distance depends upon time.

Find the equation of the line passing through the point of intersection of the lines $4x + 7y - 3 = 0$ and $2x - 3y + 1 = 0$ that has equal intercepts on the axes.

$\beta$ is the angle made by the perpendicular drawn from the origin to the line $L \equiv x+y-2=0$ with the positive $X$-axis in the anticlockwise direction. If '$a$' is the $X$-intercept of the line $L=0$ and $p$ is the perpendicular distance from the origin to the line $L=0$,then $a \tan \beta + p^2 =$

$A$ graph is drawn between the $y-x$ axes. Which of the following equations is correct for the graph?