week 4 midterm

1.Find an equation of the line that passes through the points (1, 4) and ( -7, -4)Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b.3.Solve the linear system of equationsUnique solution:Unique solution:Infinitely many solutions:4.Consider the linear programming problem.Sketch the feasible set for the linear programming problem.5.Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.one and only one solutionone and only one solutionone and only one solutioninfinitely many solutions6.Indicate whether the matrix is in row-reduced form.7.Find the pivot element to be used in the next iteration of the simplex method.8.Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.9.Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 8x = 5y + 9y = x +  y = x –  y = -x –  y = -x + 10 If the line passing through the points (2, a) and (5, – 3) is parallel to the line passing through the points (4, 8) and (- 5, a + 1) , what is the value of a? 11.MaximizeP= 10x + 12ysubject to12.Write the equation in the slope-intercept form and then find the slope and y-intercept of the corresponding line.13.Find the slope of the line that passes through the given pair of points.(2, 2) and (8, 5)14.Consider the linear programming problem.Sketch the feasible set for the linear programming problem.15.Solve the system of linear equations using the Gauss-Jordan elimination method.16.Solve the linear system of equationsUnique solution:Unique solution:Infinitely many solutions:17.Determine whether the given simplex table is in the final form. If so, find the solution to the associated regular linear programming problem.18.Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.     19.Solve the linear programming problem by the simplex method. 20.Metro Department Store’s annual sales (in millions of dollars) during 5 years wereAnnual Sales, y5.86.17.28.39Year, x12345Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L. 21.Solve the linear system of equationsUnique solution:Unique solution:Infinitely many solutions:22.Solve the system of linear equations using the Gauss-Jordan elimination method.23.Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.24.Solve the system of linear equations, using the Gauss-Jordan elimination method.25.Find the constants m and b in the linear function f(x) = mx + b so that f(1) = 2 and the straight line represented by f has slope – 1.