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

x-axis is

(a) x = 2

October 10, 2021

By Remi

1 thought on “8. The equation of a straight line passing through the point (2,-7) and parallel to<br /><br />x-axis is<br /><br />(a) x = 2<br /”

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

   [tex]\large\underline{\sf{Given- }}[/tex]

   A line

   • passes through the point (2, – 7)

   and

   • parallel to x- axis.

   [tex]\large\underline{\sf{To\:Find – }}[/tex]

   • 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

   [tex] \sf \: y – b \: = \: m(x – a)[/tex]

   [tex]\large\underline{\sf{Solution-}}[/tex]

   Given that

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

   Since,

   • Line is parallel to x- axis.

   [tex]\rm :\implies\:m \: = \: 0[/tex]

   Now,

   We know that

   • Equation of line is given by

   [tex]\rm :\longmapsto\:y – b \: = \: m(x – a)[/tex]

   where,

   [tex]\rm :\longmapsto\:a \: = \: 2[/tex]

   [tex]\rm :\longmapsto\:b \: = \: – \: 7[/tex]

   [tex]\rm :\longmapsto\:m \: = \: 0[/tex]

   On substituting all these values in above equation, we get

   [tex]\rm :\longmapsto\:y \: – \: ( – 7) = 0 \times (x – 2)[/tex]

   [tex]\rm :\longmapsto\:y + 7 = 0[/tex]

   [tex]\rm :\implies\:y \: = \: – \: 7[/tex]

   [tex]\overbrace{ \underline { \boxed { \rm \therefore The \: equation \: of \: line \: is \: y \: = \: – \: 7}}}[/tex]

   ─━─━─━─━─━─━─━─━─━─━─━─━─

   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.

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