A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.

Answer Details

To find the equation of a straight line, we need to know either two points that the line passes through or a point and the slope of the line. In this case, we are given one point that the line passes through, (-1,2), and the equation of the line, 2x+3y=6. We can use the point-slope form of the equation of a line to find the equation of the line passing through the given point. The point-slope form is: y - y1 = m(x - x1) where (x1, y1) is the given point and m is the slope of the line. To find the slope of the given line, we can rearrange the equation 2x+3y=6 into the slope-intercept form: y = (-2/3)x + 2 where the slope is -2/3. Substituting the values of the given point and slope into the point-slope form, we get: y - 2 = (-2/3)(x - (-1)) Simplifying this equation, we get: y - 2 = (-2/3)x - (2/3) Multiplying both sides by 3 to eliminate the fraction, we get: 3y - 6 = -2x - 2 Adding 2x to both sides, we get: 2x + 3y = 4 Therefore, the equation of the line passing through the given point is 2x+3y=4. Hence, the correct answer is option (D) 2x+3y=4.