Question

12. (a) Find the equation of the straight line which passes through the points (0, 1) and
(3, 13).​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

We know that,

The equation of line joining the points A and B is given by

$\boxed{ \green{\bf \:y - y_1 = \dfrac{y_2-y_1}{x_2-x_1} (x-x_1)}}$

where,

$\sf \: Coordinates \: of \: A \: and \: B \: are \: (x_1,y_1) \: and \: (x_2,y_2)$

Now,

Equation of the straight line which passes through the points (0, 1) and (3, 13) is given by

$\tt : \implies \: y - 1 = \dfrac{13 - 1}{3 - 0} (x - 0)$

$\tt : \implies \: y - 1 = \dfrac{12}{3} x$

$\tt : \implies \: y - 1 = 4x$

$\tt : \implies \: \boxed{ \pink{ \rm \: y \: = \: 4x \: + \: 1}}$

Additional Information

Additional Information Different forms of equations of a straight line

1. Equations of horizontal and vertical lines

Equation of the lines which are horizontal or parallel to the X-axis is y = a, where a is the y – coordinate of the points on the line.

Similarly, equation of a straight line which is vertical or parallel to Y-axis is x = a, where a is the x-coordinate of the points on the line

2. Point-slope form equation of line

Consider a non-vertical line L whose slope is m, A(x,y) be an arbitrary point on the line and P(a, b) be the fixed point on the same line. Equation of line is given by

y - b = m(x - a)

3. Slope-intercept form equation of line

Consider a line whose slope is m which cuts the Y-axis at a distance ‘a’ from the origin. Then the distance a is called the y– intercept of the line. The point at which the line cuts y-axis will be (0,a). Then equation of line is given by

y = mx + a.

4. Intercept Form of Line

Consider a line L having x– intercept a and y– intercept b, then the line passes through  X– axis at (a,0) and Y– axis at (0,b).

Equation of line is given by x/a + y/b = 1.

5. Normal form of Line

Consider a perpendicular from the origin having length p to line L and it makes an angle β with the positive X-axis.

Then, equation of line is given by

x cosβ + y sinβ = p.