Write the equations for the x-axis and y-axis.
For the x-axis: \( y = 0 \); for the y-axis: \( x = 0 \).
Find the equation of the line passing through the point \( (-4, 3) \) with slope \( \dfrac{1}{2} \).
\( x - 2y + 10 = 0 \)
Find the equation of the line passing through \( (0, 0) \) with slope \( m \).
\( y = mx \)
Find the equation of the line passing through \( (2, 2\sqrt{3}) \) and inclined with the x-axis at an angle of \( 75^\circ \).
\( (\sqrt{3} + 1)x - (\sqrt{3} - 1)y = 4(\sqrt{3} - 1) \)
Find the equation of the line intersecting the x-axis at a distance of 3 units to the left of the origin with slope \( -2 \).
\( 2x + y + 6 = 0 \)
Find the equation of the line intersecting the y-axis at a distance of 2 units above the origin and making an angle of \( 30^\circ \) with the positive direction of the x-axis.
\( x - \sqrt{3}y + 2\sqrt{3} = 0 \)
Find the equation of the line passing through the points \( (-1, 1) \) and \( (2, -4) \).
\( 5x + 3y + 2 = 0 \)
The vertices of \( \triangle PQR \) are \( P(2, 1) \), \( Q(-2, 3) \) and \( R(4, 5) \). Find the equation of the median through the vertex \( R \).
\( 3x - 4y + 8 = 0 \)
Find the equation of the line passing through \( (-3, 5) \) and perpendicular to the line through the points \( (2, 5) \) and \( (-3, 6) \).
\( 5x - y + 20 = 0 \)
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 this line.
\( (1 + n)x + 3(1 + n)y = n + 11 \)
Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point \( (2, 3) \).
\( x + y = 5 \)
Find the equations of the lines passing through the point \( (2, 2) \) and cutting off intercepts on the axes whose sum is 9.
\( x + 2y - 6 = 0 \) and \( 2x + y - 6 = 0 \)
Find the equation of the line through the point \( (0, 2) \) making an angle \( \dfrac{2\pi}{3} \) 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.
First line: \( \sqrt{3}x + y - 2 = 0 \); parallel line through \( (0, -2) \): \( \sqrt{3}x + y + 2 = 0 \)
The perpendicular from the origin to a line meets it at the point \( (-2, 9) \). Find the equation of the line.
\( 2x - 9y + 85 = 0 \)
The length \( L \) (in centimetre) of a copper rod is a linear function of its Celsius temperature \( C \). In an experiment, \( L = 124.942 \) when \( C = 20 \) and \( L = 125.134 \) when \( C = 110 \). Express \( L \) in terms of \( C \).
\( L = \dfrac{192}{90}(C - 20) + 124.942 \)
The owner of a milk store finds that he can sell 980 litres of milk each week at Rs 14 per litre and 1220 litres each week at Rs 16 per litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17 per litre?
\( 1340 \) litres
\( P(a, b) \) is the mid-point of a line segment between the axes. Show that the equation of the line is \( \dfrac{x}{a} + \dfrac{y}{b} = 2 \).
Point \( R(h, k) \) divides a line segment between the axes in the ratio \( 1 : 2 \). Find the equation of the line.
\( 2kx + hy = 3kh \)
By using the concept of the equation of a line, prove that the three points \( (3, 0) \), \( (-2, -2) \) and \( (8, 2) \) are collinear.