Final answer:
Step-by-step explanation:
To find the slope-intercept form of the equation of the line parallel to y = 3x - 5 and passing through the point (-1, -3), we first need to determine the slope of the given line. The slope of a line parallel to another line is always the same. So, the slope of the line we are looking for is 3. The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values, the equation becomes y = 3x + b. To find the value of b, we substitute the coordinates of the given point (-1, -3). So, -3 = 3(-1) + b. Solving for b, we get b = 0. Therefore, the equation of the line parallel to y = 3x - 5 and passing through the point (-1, -3) is y = 3x.
Similarly, to find the slope-intercept form of the equation of the line perpendicular to y = x - 4 and passing through the point (4, -5), we first need to determine the slope of the given line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. The slope of y = x - 4 is 1, so the slope of the line we are looking for is -1. Plugging in the values, the equation becomes y = -x + b. To find the value of b, we substitute the coordinates of the given point (4, -5). So, -5 = -(4) + b. Solving for b, we get b = -1. Therefore, the equation of the line perpendicular to y = x - 4 and passing through the point (4, -5) is y = -x - 1.