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

1.	8. The equation of a straight line passing through the point (2,-7) and parallel tox-axis is(a) x = 2(c) y-7(b) x -7(d) y 2
Answer» 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 $\rm :\longmapsto\:y \: - \: ( - 7) = 0 \times (x - 2)$ $\rm :\longmapsto\:y + 7 = 0$ $\rm :\implies\:y \: = \: - \: 7$ $\overbrace{ \underline { \boxed { \rm \therefore The \: equation \: of \: line \: is \: y \: = \: - \: 7}}}$ ─━─━─━─━─━─━─━─━─━─━─━─━─ 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.

8. The equation of a straight line passing through the point (2,-7) and parallel tox-axis is(a) x = 2(c) y-7(b) x -7(d) y 2

Answer»

Correct Statement is

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

(a) x = 2

(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.