Equation of a Line
The equation of a line is a linear relation between two variables x and y, which is satisfied by the coordinates of each & every point on the line and not by any other point.
There are various forms of Equation of a line.
- 2x + 3y + 7 = 0 which can also be written as 2x + 3y = (-7).
- 4x + 3 = 7 where B = 0.
- 3y + 2 = 5 where A = 0.
Point Slope Form
Equation of a line with slope or gradient m and passing through the point (,) is given by
( – ) = ( – )
- Equation of line passing from origin (0, 0) and slope 1 is (y – 0) = (x – 0) or y = x.
- Equation of line passing from (1, 3) and slope 4 is (y – 3) = 4(x – 1) or y – 3 = 4x – 4
Hence the line is given by the equation 4x – y – 1 = 0.
Slope Intercept form
The length of the intercept made by of a line on the Y-axis is called its y-intercept.
Equation of a line with slope or gradient m and making an y intercept of c units is given
by (y – c) = m ( x – 0 )
i.e y=mx + c
- Equation of line with slope, m = & y-intercept c = 7 is y = x + 7.
- Equation of line with slope, m = 11 & y-intercept c = -2 is y = 11x – 2.
- Write the equation of the line 3x = 4y + 7 in general form.
- Convert the equation 3x = 4y + 2 in slope intercept form.
- Find the equation of the line passing from origin (0, 0) and slope 4.
- Find the equation of the line passing from origin (1, 5) and slope -7.
- Find the equation of the line with slope 2 & y-intercept 11.
- Find the equation of the line with slope & y-intercept -5.
- 3x – 4y – 7 = 0.
- Y = x –
- y = 4x
- 7x + y – 12 = 0.
- y = 2x + 11
- y = x – 5 or 3x – 7y – 35=0.
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