Solutions to the line problems are presented along with detailed explanations .
Solution to Problem 1: The slope of the line is given by m = (y2 - y1) / (x2 - x1) = (12 - 0) / (-4 - (-1)) = - 12 / 3 = - 4 We now write the equation of the line in point slope form: y - y1 = m (x - x1) y - 0 = - 4(x - (-1)) Simplify and write the equation in general form y + 4x = - 4
Solution to Problem 2: The two points have the same x coordinate and are on the same vertical line whose equation is x = - 2
Solution to Problem 3: The two points have the same y coordinate and are on the same horizontal line whose equation is y = 5
Solution to Problem 4: A line parallel to the axis has equation of the form y = constant. Since the line we are trying to find passes through (3 , 4), then the equation of the line is given by: y = 4
Solution to Problem 5: The x intercept is the point (-1 , 0). The slope of the line is given by: m = (2 - 0) / (-3 - (-1)) = 2 / - 2 = -1 The point slope form of the line is y - 0 = -1(x - (-1)) The equation can be written as y = - x - 1
Solution to Problem 6: The x and y intercepts are the points (-4 , 0) and (0 , 5). The slope of the line is given by: m = (5 - 0) / (0 - (-4)) = 5 / 4 The point slope form of the line is y - 5 = (5 / 4)(x - 0) Multiply all terms by 4 and simplify 4 y - 20 = 5 x
Solution to Problem 7: The line y = 9 is a horizontal line (parallel to the x axis). The line that is perpendicular to the line y = 9 have the form x = constant. Since the (-1 , 0) is a point on this line, the equation is given by x = -1
Solution to Problem 8: To find the slope of the given, we first write in slope intercept form 5y = 3x + 8 y = (3/5)x + 8/5 The slope is equal to 3/5. The y intercept is found by setting x = 0 in the equation and solve for y. Hence the y intercept is at y = 8/5. The x intercept is found by setting y = 0 and solve for x. Hence the x intercept is at x = -8/3
Solution to Problem 9: Given the equation x / 4 - y / 5 = 3 Keep only the term in y on the left side of the equation - y / 5 = 3 - x / 4 Multiply all terms by -5 y = (5/4)x - 15
Solution to Problem 10: The line x = - 3 is parallel to the y axis and the line x = 0 is the y axis. The two lines are parallel.
Solution to Problem 11: For a point to be on a line, its coordinates must satisfy the equation of the line. 2 - 4(2b) = 6 Solve for b b = -1/2
