Page 142 - DMTH201_Basic Mathematics-1

Unit 5: Equations of Straight Lines

Notes
Figure 5.14

Thus, the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if
y = mx + c …(3)
Note that the value of c will be positive or negative according as the intercept is made on the
positive or negative side of the y-axis, respectively.
Case II: Suppose line L with slope m makes x-intercept d. Then equation of L is
y = m(x d ) ...(4)
Students may derive this equation themselves by the same method as in Case I.

1
Example: Write the equation of the lines for which tan , where is the inclination
2
3
of the line and (i) y-intercept is (ii) x-intercept is 4.
2
Solution:
1 3
(i) Here, slope of the line is m tan and y - intercept c .
2 2
Therefore, by slope-intercept form (3) above, the equation of the line is

1 3
y = x or 2y x 3 0,
2 2
which is the required equation.

1
(ii) Here, we have m tan and d = 4.
2
Therefore, by slope-intercept form (4) above, the equation of the line is

1
y = (x 4) or 2y x 4 0,
2
which is the required equation.

5.3.5 Intercept - Form

Suppose a line L makes x-intercept a and y-intercept b on the axes, and L meets x-axis at the point
(a, 0) and y-axis at the point (0,b) (Figure 5.15). By two-point form of the equation of the line, we
b 0
have y 0 (x a ) or ay bx ab ,
0 a

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