Maharashtra Board Solutions for Chapter: Straight Line, Exercise 2: EXERCISE 5.2

If the $X$ and $Y$-intercepts of line $L$ are $2$ and $3$ respectively then find the slope of line $L$.

Find the slope of the line whose inclination is $30°$.

Find the slope of the line whose inclination is $\frac{\mathrm{\pi }}{4}$ .

Find the slope of the line which makes an angle of $45°$ with the positive direction of the $Y$-axis measured anticlockwise.

Find the value of $k$ for which points $P\left(k,-1\right),$ $Q\left(2,1\right)$ and $R\left(4,5\right)$ are collinear.

Find the acute angle between the $X$-axis and the line joining points $A\left(3,-1\right)$ and $B\left(4,-2\right)$.

A line passes through points $A\left(x_1,y_1\right)$ and $B\left(h,k\right)$. If the slope of the line is $m$ then show that $k-y_1=m\left(h-x_1\right)$.

If points $\mathrm{A}(h,0),\mathrm{B}(0,k)\text{ and }\mathrm{C}(a,b)$ lie on a line then show that $\frac{a}{h}+\frac{b}{k}=1$.