Question

the equation of line passing through (2, 3) and having slope is 1/2 is

x-y+6=0
x-2y+4=0
5x-5y+9=0
2x-y+3=0​

Answer 1

$\large\underline{\sf{Given- }}$

Line passing through

• a point (2, 3)

and

• having slope is 1/2

$\large\underline{\sf{To\:Find - }}$

• The equation of line.

Concept Used :-

Slope - point form of Line

Let us assume a line which passes through the point (a, b) having slope 'm', then equation of line is

$\sf \: y - b \: = \: m(x - a)$

$\large\underline{\sf{Solution-}}$

Given that

• A line passing through the point (2, 3) and having slope is 1/2.

We know that,

• The equation of line is given by

$\rm :\longmapsto\:y - b \: = \: m(x - a)$

where,

$\rm :\longmapsto\:a \: = \: 2$

$\rm :\longmapsto\:b \: = \: 3$

$\rm :\longmapsto\:m \: = \: \dfrac{1}{2}$

Now, Substituting all the values, we get

$\rm :\longmapsto\:y - 3 = \dfrac{1}{2} (x - 2)$

$\rm :\longmapsto\:2y - 6 = x - 2$

$\rm :\longmapsto\:x - 2y - 2 + 6 =0$

$\rm :\longmapsto\:x - 2y + 4 = 0$

$\overbrace{ \underline { \boxed { \rm \therefore The \: equation \: of \: line \: is \: x - 2y + 4 = 0)}}}$

─━─━─━─━─━─━─━─━─━─━─━─━─

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 b 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, the equation of line is given by x cosβ + y sinβ = p.