2x+y−3=0 is it an equation of a straight line

Mathematics

ScanSolve AI Answer

Answer

Yes\text{Yes}

Step-by-step solution

3 steps

Yes, 2x+y−3=02x+y-3=0 is an equation of a straight line.

  1. Identify the characteristics of a linear equation.

    An equation represents a straight line if the highest power of both variables (xx and yy) is 1, and there are no products of variables (like xyxy).

  2. Rearrange the given equation into the slope-intercept form (y=mx+cy=mx+c).

    Given the equation:

    2x+y−3=02x+y-3=0

    To isolate yy, subtract 2x2x and add 3 to both sides:

    y=−2x+3y = -2x + 3
  3. Compare with the slope-intercept form.

    The equation y=−2x+3y = -2x + 3 is in the form y=mx+cy=mx+c, where m=−2m=-2 (the slope) and c=3c=3 (the y-intercept). Since it can be expressed in this form, it represents a straight line.

    The answer is Yes\text{Yes}.

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