Question

8. The equation of a straight line passing through the point (2,-7) and parallel to

x-axis is

(a) x = 2

(c) y-7

(b) x -7

(d) y 2​

Answer 1

Correct Statement is

The equation of a straight line passing through the point (2,-7) and parallel to x-axis is

(a) x = 2

(c) y = - 7

(b) x = 7

(d) y = 2

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

A line

• passes through the point (2, - 7)

and

• parallel to x- axis.

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

• Equation of line.

Concept Used :-

Slope - point form of a line

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

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

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

Given that

• A line passes through the point (2, - 7) and parallel to x - axis.

Since,

• Line is parallel to x- axis.

$\rm :\implies\:m \: = \: 0$

Now,

We know that

• Equation of line is given by

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

where,

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

$\rm :\longmapsto\:b \: = \: - \: 7$

$\rm :\longmapsto\:m \: = \: 0$

On substituting all these values in above equation, we get

$\rm :\longmapsto\:y \: - \: ( - 7) = 0 \times (x - 2)$

$\rm :\longmapsto\:y + 7 = 0$

$\rm :\implies\:y \: = \: - \: 7$

$\overbrace{ \underline { \boxed { \rm \therefore The \: equation \: of \: line \: is \: y \: = \: - \: 7}}}$

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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.

Answer 2

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