Final answer:
To find the equations of lines parallel to the given line and passing through the point (4,5), we first determine the slope of the given line and then use the point-slope form of a line to find the equation. The slope of the given line is 2/3, so the equations of the parallel lines are y - 5 = (2/3)(x - 4).
Step-by-step explanation:
To find the equations of those straight lines which pass through the point (4,5) and are parallel to the line 2x-3y-5=0, we need to first determine the slope of the given line. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. In this case, we rearrange the given equation to solve for y: 3y = 2x - 5, y = (2/3)x - (5/3). Therefore, the slope of the given line is 2/3.
Since the lines we are looking for are parallel to the given line, they will have the same slope of 2/3. The point-slope form of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line. Plugging in the coordinates (4,5) and the slope 2/3, we get the equation of the line: y - 5 = (2/3)(x - 4).