The line y =3x-5 meet x-axis at the point m. the line 3y+2x=2 meets y-axis at point n. find the equation of the line joining m and n in the form ax + by + c = 0 where: a, b,c are integers.

Answer-

The line equation is,

Solution-

The line meets x-axis at the point M, i.e M is the x-intercept of this line. At the x-intercept y=0, so

So, coordinate of M is

The line meets y-axis at point N, i.e N is the y-intercept of this line. At the y-intercept x=0, so

So, coordinate of N is

The line joining M and N can be found out by applying two point formula of straight line,

As it is given that all the coefficients are integers, so multiplying with 3

Solution: As given  line y =3x-5 meet x-axis at the point M.

  On x axis y coordinate is zero.

Put y =0 in above equation, we get →x = 5/3

∴ Coordinate of M is (5/3,0).

As, also given , line 3y+2x=2 meets y-axis at point N.

On y axis , x coordinate is zero.

Substituting , x=0 in above equation, gives y =2/3.

Coordinate of point N is (0,2/3).

Equation of line passing through two points (a,b) and (p,q) is given  by

       →

Or as X intercept = 5/3, and Y intercept = 2/3

Equation of line in intercept form is →, where a and b is X intercept and y intercept respectively.

So, line passing through (5/3,0) and (0,2/3) is given by

→

 →  

→ 6 x + 15 y =10 [Taking LCM of 5 and 2 which is 10]

→ 6 x + 15 y -10=0, which is equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this