Final answer:
To find the equation of the straight lines that pass through (1, -4) and make a 45° angle with the given line, we can find the slopes of the lines using the property that the product of the slopes of two perpendicular lines is -1. The equations of the lines are y = (3/2)x - 1/2 and y = (-3/2)x - 6.
Step-by-step explanation:
To find the equation of the straight lines that pass through (1, -4) and make an angle of 45° with the line 2x+3y+7=0, we can use the concept of slope. The given line has a slope of -2/3. To find the slope of the lines that make a 45° angle, we can use the fact that the product of the slopes of two perpendicular lines is -1. Therefore, the slopes of the lines we are looking for are 3/2 and -3/2.
Using the point-slope form of a line, we can write the equations of the lines as y - (-4) = (3/2)(x - 1) and y - (-4) = (-3/2)(x - 1). Simplifying these equations gives us y = (3/2)x - 1/2 and y = (-3/2)x - 6.