Final answer:
To write the point-slope form of the equation of a line and convert it to slope-intercept form.
Step-by-step explanation:
To write the point-slope form of the equation of the line, we need to use the formula: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
A) For the line parallel to y = x + 5, which has a slope of 1, and passes through (-5, -1), the point-slope form is y - (-1) = 1(x - (-5)). Simplifying, we get y + 1 = x + 5.
B) For the line parallel to y = -2x + 5, which has a slope of -2, and passes through (4, -5), the point-slope form is y - (-5) = -2(x - 4). Simplifying, we get y + 5 = -2x + 8.
C) For the line perpendicular to y = 2x - 2, which has a slope of -1/2 (negative reciprocal of 2), and passes through (-4, 0), the point-slope form is y - 0 = -1/2(x - (-4)). Simplifying, we get y = -1/2x + 2.
D) For the line perpendicular to y = -x - 1, which has a slope of 1 (negative reciprocal of -1), and passes through (5, -3), the point-slope form is y - (-3) = 1(x - 5). Simplifying, we get y + 3 = x - 5.
To convert the point-slope form to slope-intercept form (y = mx + b), we can solve for y.
A) From y + 1 = x + 5, we can subtract 1 from both sides to get y = x + 4.
B) From y + 5 = -2x + 8, we can subtract 5 from both sides to get y = -2x + 3.
C) From y = -1/2x + 2, no further simplification is needed.
D) From y + 3 = x - 5, we can subtract 3 from both sides to get y = x - 8.