Step-by-step explanation:
Hey there!
1.no Ans:
The equation of a st.line passing through point (3,0) is;
(y-0) = m1(x-3)........(i)
Another equation is,
y = 2/3x+1...........(ii)
Comparing the equation (ii) with y= mx+c. We get;
Slope (m2)= 2/3
As they are parallel lines, m1=m2.
So, putting value of m1 in equation (i).
[tex]y = \frac{2}{3} (x - 3)[/tex]
[tex]y = \frac{2}{3} x - 3 \times \frac{2}{3} [/tex]
Therefore the required equation is; y = 2/3x -2.
2.Ans:
The equation of a st.line passing through (4,1) is;
(y-1) = m1(x-4)...........(i)
y = -1/2x +2...............(ii)
From equation (ii)
y = -1/2x+2
Comparing the equation with y = mx+c
Slope (m2)= -1/2
As they are equal m1=m2= -1/2
Putting value of slope in equation (i)
[tex](y - 1) = \frac{ - 1}{2} (x + 2)[/tex]
[tex]2(y - 1) = - 1(x + 2)[/tex]
[tex]2y - 2 = - x - 2[/tex]
[tex]x + 2y = 0[/tex]
Therefore the required equation is; x+2y=0.
3. no. Ans:
The equation of a st.line passing through point (-1,-1) is ;
(y+1)= m1(x+1)..........(i)
y= -2x-4.....................(ii)
From equation (ii)
Comparing the equation with y = mx+c.
Slope(m2)= -2
As they are parallel lines, m1=m2 = -2.
Putting value of slope in equation (i)
[tex](y + 1) = - 2(x + 1)[/tex]
[tex]y + 1 = - 2x - 2[/tex]
[tex]2x + y + 3 = 0[/tex]
Therefore the required equation is 2x+y+3=0.
4.no Ans:
The equation of a st.line passing through (-4,-5) is;
(y+5) = m1(x+4)..........(i)
y = -2x-5...............(ii)
From equation (ii)
Comparing the equation with y = mx+c, we get;
Slope (m2)= -2
As they are parallel lines, m1=m2= -2
Putting value of slope in equation (i)
[tex](y + 5) = - 2(x + 4)[/tex]
[tex]y + 5 = - 2x - 8[/tex]
[tex]2x + y + 13 = 0[/tex]
Therefore the required equation is 2x+y+13=0.
5.no Ans:
The equation of a st.line passing through (-4,3) is:
(y-3)= m1(x+4).........(i)
y = 1/2x-3.......(ii)
From equation (ii)
Comparing the equation with y= mx+c.
Slope (m2) = 1/2
As they are parallel lines, m1=m2 = 1/2.
Putting value of slope in equation (i)
[tex](y - 3) = \frac{1}{2} (x + 4)[/tex]
[tex]2(y - 3) = x + 4[/tex]
[tex]2y - 6 = x + 4[/tex]
[tex]x - 2y + 10 = 0[/tex]
Therefore the required equation is; x-2y+10=0.
6.no. Ans;
The equation of a st.line passing through (5,-5) is;
(y+5)= m1(x-5)............(i)
y = -3/2x+2......(ii)
Comparing the equation (ii) with y = mx+c.
Slope(m2)= -3/2.
As they are parallel lines, m1=m2= -3/2.
Putting value of slope in equation (i)
[tex](y + 5) = \frac{ - 3}{2} (x - 5)[/tex]
[tex]2(y + 5) = - 3(x - 5)[/tex]
[tex]2y + 10 = - 3x + 15[/tex]
[tex]3x + 2y - 5 = 0[/tex]
Therefore the required equation is; 3x+2y-5=0.
Hope it helps...
