Slope Intercept Form of a Line

Q. Find the equation of a line making an angle of ${150}^o$ with the $x-axis$ and cutting off intercept $2$ from $y-axis$

1. $\sqrt{3}x+y=2\sqrt{3}$
2. $2\sqrt{3}x+\sqrt{3}y=2\sqrt{3}$
3. $\sqrt{3}x-y=2\sqrt{3}$
4. $x+\sqrt{3}y=2\sqrt{3}$

Q. The intercept made by a line on y-axis is double to the intercept made by it on x-axis. If it passes through $(1,2)$ then its equation.

1. $2x+y=4$
2. $2x+y+4=0$
3. $2x-y=4$
4. $2x-y+4=0$

Q.

The equation of the straight line which makes an angle of ${15}^{\circ }$ with the positive direction of x-axis and cuts an intercept of length 4 on the negative direction of y-axis, is

1. 

2. 

3. 

4. 

Q.

A line cuts the x - axis at A(7, 0) and the y - axis at B(0, -5). A variable line PQ is drawn perpendicular to AB. Cutting the x - axis at P and the y - axis at Q.
If AQ and BP intersect at R, the locus of R is

1. none of these

2. $x^2+y^2-7x+5y=0$

3. $x^2+y^2+7x-5y=0$

4. 5x - 7y = 35

Q. Equation of image of line $x+y={\sin }^{-1}(a^6+1)+{\cos }^{-1}(a^4+1)-{\tan }^{-1}(a^2+1),a\in R$ about x-axis is given by

1. $x-y=0$
2. $x-y=\frac{\pi }{2}$
3. $x-y=\pi$
4. $x-y=\frac{\pi }{4}$

Q.

Find the equations of the line through the point (3, 2)
which make an angle of ${45}^{\circ }$ with the line $x-2y-3=0$

Q. Find the equation to the straight line:
cutting off intercepts $3$ and $2$ from the axes.

Q. The intercepts made by the line $2x-3y+12=0$ on the co-ordinate axis are

1. None of these
2. $x-$ intercept $=-6$ and $y-$ intercept $=4$
3. $x-$ intercept $=4$ and $y-$ intercept $=-6$
4. $x-$ intercept $=-3$ and $y-$ intercept $=2$