Question

Write an equation for the line parallel to 6x – 3y = 9 that contains (-5,-8).

Write an equation for the line parallel to 2x – 18 – 3y = 0 that contains (9,-3).
Write an equation for the line perpendicular to 5x + 2y = 1 that contains (3,4).
Write an equation for the line perpendicular to 4x + y = 3 that contains (8,-1).

Answer 1

To find an equation for a line parallel to a given line, use the same slope and plug in the given point in the point-slope form. To find an equation for a line perpendicular to a given line, use the negative reciprocal slope and plug in the given point in the point-slope form.

Step-by-step explanation:

To find an equation for a line parallel to a given line, we need to find a line with the same slope as the given line. The given line has an equation 6x – 3y = 9 with a slope of 2. To find the equation of the parallel line that contains the point (-5,-8), we can use the point-slope form of a line equation: y - y1 = m(x - x1). Plugging in the values, we get y + 8 = 2(x + 5), which simplifies to y = 2x + 2.

To find an equation for a line perpendicular to a given line, we need to find a line with a negative reciprocal slope of the given line. The given line has an equation 5x + 2y = 1 with a slope of -5/2. To find the equation of the perpendicular line that contains the point (3,4), we can use the point-slope form of a line equation: y - y1 = m(x - x1). Plugging in the values, we get y - 4 = -2/5(x - 3), which simplifies to y = -2/5x + 22/5.