Detailed solutions to algebra problems are presented.
Solution to Problem 5:Given the equation 2 x  4 y = 9 To find the x intercept we set y = 0 and solve for x. 2 x  0 = 9 Solve for x. x = 9 / 2 The x intercept is at the point (9/2 , 0). Solution to Problem 6:Given the function f(x) = 6 x + 1 f(2)  f(1) is given by. f(2)  f(1) = (6 × 2 + 1)  (6 × 1 + 1) = 6 Solution to Problem 7:Given the points (1, 1) and (2 , 2), the slope m is given by m = (y2  y1) / (x2  x1) = (2  (1)) / (2  (1)) = 1 Solution to Problem 8:Given the line 5x  5y = 7 Rewrite the equation in slope intercept form y = m x + b and identify the value of m the slope.  5y =  5x + 7 y = x  7/5 The slope is given by the coefficient of x which is 1. Solution to Problem 9:To find the equation of the line through the points (1 , 1) and (1 , 2), we first use the slope m. m = (y2  y1) / (x2  x1) = (2  (1)) / (1  (1)) = 3 / 0 The slope is undefined which means the line is perpendicular to the x axis and its equation has the form x = constant. Since both points have equal x coordinates 1, the equation is given by: x = 1 Solution to Problem 10:The equation to solve is given by. 2 x + 2 3 = 3 Add 3 to both sides of the equation and simplify. 2 x + 2 = 0 2 x + 2 is equal to 0 if 2 x + 2 = 0. Solve for x to obtain x = 1
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