Find the equation of the line parallel to 2y = 3(x - 2) and passes through the point (2, 3)

Answer Details

To find the equation of a line that is parallel to another line and passes through a specific point, we can use the slope-point form of a line. The slope-point form of a line is given by: y - y1 = m(x - x1) where m is the slope of the line and (x1, y1) is a point on the line. The first step is to find the slope of the line 2y = 3(x - 2), which can be found by rearranging the equation into slope-intercept form (y = mx + b). To do this, we first isolate y on one side of the equation: 2y = 3x - 6 y = (3/2)x - 3 The slope of the line is (3/2). Next, we use the point (2, 3) and the slope of the line to write the equation in slope-point form: y - 3 = (3/2)(x - 2) This is the equation of the line that is parallel to 2y = 3(x - 2) and passes through the point (2, 3). So, the correct answer is y = (3/2)x - 3.