Various Forms of the Equation of a Line

The equations of the normal to the curve  $x=1-\cos \theta :y=\theta -\sin \theta$ at $\theta =\frac{\pi }{4}$  would be:

If a line with positive slope passing through $(-1, 4)$ meets the coordinate axis at $P$ and $Q$, then the minimum value of $\left|OP\right|+\left|OQ\right|$ is ($O$ being origin).

The owner of a medical store finds that, he can sell $1550$ litres of hand sanitizer each week at Rs. $550$/litre and $2430$ litres of hand sanitizer each week at Rs. $750$/litre. Assuming a linear relationship between selling price and demand, the number of litres the owner could sell weekly at Rs. $950$/litre is

The equation of straight line passing through $(-2, -1)$ and making an angle of $60°$ from ordinate in counter clockwise direction is given by

The equation of the line passing through the origin and which bisects the portion of the line $3x+y=6$ intercepted between the co−ordinate axes is of the form $ax+by=0$, then find the value of $a+b$.

Upen draw a line on his notebook whose equation is $4\mathrm{x}-5\mathrm{y}+3=0$. What are the coordinates of the point(s) on this line at a distance of $15$ units from the point $\mathrm{P}(2,2)$?

Shyam draws a straight line on a piece of paper which makes an acute angle $\text{'}\mathrm{\alpha }\text{'}$ with the positive direction of $\mathrm{x}$ axis. He made it to pass through the point $\mathrm{M}(4, 5)$. This line meets the line $\mathrm{x}=8$ at the point $\mathrm{P}$ and line $\mathrm{y}=4$ at the point $\mathrm{Q}$, then find which option holds well?

The equations of the lines which make intercepts on the axes whose sum is $8$ and product is $15$ are

If $\left(a,-2a\right), a>0$ is the midpoint of a line segment intercepted between the co-ordinate axes, then the equation of the line is

If the portion of a line intercepted between the coordinate axes is divided by the point $\left(2,-1\right)$ in the ratio $3:2$, then the equation of that line is

The equation of the line through the point $\left(2,3\right)$ such that its $x$-intercept is twice of its $y$ intercept, is

Find the equations of the lines, whose slope$=-4$ and y-intercept $=3$

Find the equation of the line, whose slope$=-3$ and y-intercept$=4$

For each equation given below, find the slope and y-intercept: $x=3y+5$

For equation given below, find the slope and y-intercept: $x+y+2=0$

For equation given below, find the slope and y-intercept: $3x-y-8=0$

For equation given below, find the slope and y-intercept: $2x+y+4=0$