Question

The equation of a straight line which passes through the point (1,−2) and cuts off equal intercept from axes will be:

1. x+y=1
2. x-y=1
3. x+y+1=0
4. x-y-2=0

Answer 1

The equation of a straight line that passes through the point (1, -2) and cuts off equal intercepts from the axes is x + y + 1 = 0.

Step-by-step explanation:

The question asks to find the equation of a straight line that passes through the point (1, −2) and cuts off equal intercepts from the x-axis and y-axis. To solve this, we need to understand that if a line cuts off equal intercepts on the axes, then its x-intercept (a) and y-intercept (b) are equal (let's say both are c). The general equation of a line with intercepts is of the form x/a + y/b = 1. Since we know a = b = c, our equation simplifies to x/c + y/c = 1, or x + y = c. We have the point (1, −2) which lies on the line, so by substituting x = 1 and y = −2 into the equation we get: 1 + (−2) = c, thus c = −1. Therefore, the equation of our line becomes x + y = −1, which rearranges to x + y + 1 = 0.