Question

Find the equations of the straight lines passing through the point (-3, 2) and making an
angle of 45° with the straight line 3x-y+4=0.​

Answer 1

Answer:

y= x÷2 + 7÷2

Step-by-step explanation:

The slope of the given line =3

Let the slope of the unknown line be m

As the angle between both the lines is 45°, we can apply tanФ= (3-m)÷(1+3m)

tan 45=1

1+3m=3-m

4m=2

m=1÷2

The points are (-3, 2)

Applying the equation

y=mx+c

Substituing the values of x, y and m we get the constant c

2=-3÷2 +c

c=7÷2

Answer 2

Answer:

y= x÷2 + 7÷2

Step-by-step explanation:

The slope of the given line =3

Let the slope of the unknown line be m

As the angle between both the lines is 45°, we can apply tanФ= (3-m)÷(1+3m)

tan 45=1

1+3m=3-m

4m=2

m=1÷2

The points are (-3, 2)

Applying the equation

y=mx+c

Substituing the values of x, y and m we get the constant c

2=-3÷2 +c

c=7÷2