Question

1.) through: (3,0), parallel to y=2/3x+1

Answer 1

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).

$y = \frac{2}{3} (x - 3)$

$y = \frac{2}{3} x - 3 \times \frac{2}{3}$

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)

$(y - 1) = \frac{ - 1}{2} (x + 2)$

$2(y - 1) = - 1(x + 2)$

$2y - 2 = - x - 2$

$x + 2y = 0$

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)

$(y + 1) = - 2(x + 1)$

$y + 1 = - 2x - 2$

$2x + y + 3 = 0$

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)

$(y + 5) = - 2(x + 4)$

$y + 5 = - 2x - 8$

$2x + y + 13 = 0$

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)

$(y - 3) = \frac{1}{2} (x + 4)$

$2(y - 3) = x + 4$

$2y - 6 = x + 4$

$x - 2y + 10 = 0$

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)

$(y + 5) = \frac{ - 3}{2} (x - 5)$

$2(y + 5) = - 3(x - 5)$

$2y + 10 = - 3x + 15$

$3x + 2y - 5 = 0$

Therefore the required equation is; 3x+2y-5=0.

Hope it helps...