Question

One of the equation of the lines which passes through the point (-2, 3) and equally inclined to the co-ordinate axes is .

• A. $y=x+5$
• B. $y=x+4$
• C. $y=-x-1$

Answer 1

The correct option is A $y=x+5$

From the above diagram it is clear that; there are two lines PQ and RS, equally inclined to the co-ordinate axes.

For line PQ: m = tan 45° = 1

and $(x_1,y_1)=(-2,3)$

Therefore, its equation: $(y–y_1)=m(x–x_1)$
⟹ $y–3=1(x+2)$

⟹ $y-3=x+2$

⟹ y = x + 5

For line RS: m = tan (-45°) = -1

and$(x_1,y_1)=(-2,3)$

Therefore, its equation: $(y–y_1)=m(x–x_1)$

⟹ $y–3=-1(x+2)$

⟹ $y-3=-x-2$

⟹ $y=-x+1$

Therefore, the required equations are $y=x+5andy=-x+1$