Find the equation of the line which passes through the point (1, -2) and cuts off equal intercepts from the axes.
Understand the Problem
The question is asking for the equation of a line that passes through the point (1, -2) and has equal intercepts from the axes. This involves finding the slope and using the intercept form of the equation of a line.
Answer
The equation of the line is $x + y = -1$.
Answer for screen readers
The equation of the line is $x + y = -1$.
Steps to Solve
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Identify the form of the equation The equation of a line with equal intercepts is of the form $x + y = a$, where $a$ is the length of the intercepts on both axes.
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Find the intercepts Given that the intercepts are equal, let's denote the intercepts as $c$. Then, we can express the equation as $x + y = c$.
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Substitute the point into the equation Since the line passes through the point (1, -2), substitute these coordinates into the equation: $$ 1 + (-2) = c $$ This simplifies to: $$ c = -1 $$
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Write the final equation Now that we know $c$, we can write the final equation of the line: $$ x + y = -1 $$
The equation of the line is $x + y = -1$.
More Information
The line with equal intercepts has symmetry with respect to both axes. In this case, the intercepts are at (-1, 0) on the x-axis and (0, -1) on the y-axis. This means the distances from the origin to the x-intercept and y-intercept are the same.
Tips
- Miscalculating the intercepts by not recognizing that they are equal.
- Confusing the signs when substituting the point into the equation.
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