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प्रश्न
Draw the graph of the following line:
x + 3 = 0
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उत्तर
To graph the line x + 3 = 0, we first isolate the variable x to find its standard form.
1. Solve for x
Subtract 3 from both sides of the equation:
x + 3 – 3 = 0 – 3
x = –3
2. Identify the type of line
The equation x = –3 represents a vertical line. In this equation, the value of x is always –3, regardless of the value of y.
3. Determine key features
x-intercept: The line crosses the x-axis at the point (–3, 0).
Slope: The slope (m) of a vertical line is undefined because the “run” (change in x) is zero and division by zero is undefined.
y-intercept: Since the line is parallel to the y-axis and located at x = –3, it never crosses the y-axis. Therefore, there is no y-intercept.
4. Plot the Line
To draw the graph, locate 3 on the x-axis and draw a straight vertical line passing through it. Every point on this line, such as (3, 2), (–3, 0) and (–3, 5), satisfies the original equation.
