**Write the equations for the x-and y-axes.Q1:-**

**Equation of the x-axis**:
Along the x-axis, the value of y is always 0, regardless of x. Therefore, the equation is:

$$y=0\mathrm{\mathrm{}}$$

**Equation of the y-axis**: Along the y-axis, the value of $x$ is always 0, regardless of $y$. Therefore, the equation is:$$x=0$$

**Q2:-**Passing through the point (– 4, 3) with slope 1/2.

**Q3:-**Passing through (0, 0) with slope m.

**Q4:-**To find the equation of the line passing through the point $(2, 2\sqrt{3})$ and inclined at an angle of $75^\circ$

**Intersecting the x-axis at a distance of 3 units to the left of the origin with slope –2.Q5:-**

**Point of Intersection**: Since the line intersects the x-axis 3 units to the left of the origin, the end of intersection with the x-axis is $(-3,0)$.

**Slope**: The slope of the line is given as $m=-2$.

**Equation of the Line**:
Using the point-slope form of the equation of a line:

$$y-{y}_{1}=m(x-{x}_{1})$$

where $({x}_{1},{y}_{1})=(-3,0)$ and $m=-2$ we get:

Simplifying this:

$$y=-2(x+3)$$$$y=-2x-6$$Thus, the equation of the line is:

$y = -2x - 6$**Q7:**-Passing through the points (–1, 1) and (2, – 4).

**Q9:**-Find the equation of the line passing through (–3, 5) and perpendicular to the line through the points (2, 5) and (–3, 6).

**Q10:-**A line perpendicular to the line segment joining the points (1, 0) and (2, 3) divides it in the ratio 1: n. Find the equation of the line

**Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the points (2, 3)Q11:-**

**Q12:-**Find the equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

**Q13:-**Find the equation of the line through the point (0, 2) making an angle 2Ï€/ 3 with the positive x-axis. Also, find the equation of the line parallel to it and crossing the y-axis at a distance of 2 units below the origin.

**Q14:-**The perpendicular from the origin to a line meets it at the point (–2, 9), find the equation of the line.

**Q15:-**The length L (in centimetres) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L= 125.134 when C = 110, express L in terms of C.

**The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?Q16:-**

**Q17:-**P (a, b) is the mid-point of a line segment between axes. Show that the equation of the line is (x/a)+(y/b)=2.

**Q18:**-Point R (h, k) divides a line segment between the axes in the ratio 1: 2. Find an equation of the line.

**Q19:-**By using the concept of equation of a line, prove that the three points (3, 0), (– 2, – 2) and (8, 2) are collinear