7. Find the equation of a line of gradient -2 at appoint (4,3) 3marks 8. SECTION II (40 MARKS)ANSWER ANY TWO QUESTIONS 1ai) Explain the properties of a set using diagrams (8marks) ii) What are rational numbers giving examples (2marks?) b) Factorize the following using quadratic formula 9X^wedge 2+4X-2 (4marks) 4X^wedge 2+3X-8 (3marks) X^wedge 2+X-4 (3 marks) 2. Solve the following simultaneous equation using substitutional method 1) 2X+3Y=4 (4marks) 4X+2Y=6 ii) x+2y=4 (4 marks) 3x+2y=8 iii) Using elimination method solve (4marks) 2x+3y=4 3x+2y=6 b. i) what is a matrix (1mark)

7. The equation of a line with gradient -2 passing through the point (4,3) can be found using the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the gradient and (x1, y1) is the given point. Substituting the values, we get y - 3 = -2(x - 4). Simplifying this equation, we get y = -2x + 11.<br /><br />8. <br />SECTION II (40 MARKS) ANSWER ANY TWO QUESTIONS<br /><br />1ai) The properties of a set can be explained using diagrams by representing the elements of the set as points or circles in a Venn diagram. The properties include closure, associativity, commutativity, distributivity, and identity.<br /><br />ii) Rational numbers are numbers that can be expressed as a fraction where both the numerator and denominator are integers. Examples include 1/2, -3/4, and 5.<br /><br />b) Factorizing the given quadratic equations using the quadratic formula:<br />$9X^2+4X-2$ can be factored as $(3X-2)(3X+1)$<br />$4X^2+3X-8$ can be factored as $(4X-8)(X+1)$<br />$X^2+X-4$ can be factored as $(X-1)(X+4)$<br /><br />2. Solving the simultaneous equations using the substitution method:<br />1) For the equations $2X+3Y=4$ and $4X+2Y=6$, we can solve for X in terms of Y from the first equation and substitute it into the second equation to find the value of Y. Then, we can substitute the value of Y back into the first equation to find the value of X.<br /><br />ii) For the equations $x+2y=4$ and $3x+2y=8$, we can solve for x in terms of y from the first equation and substitute it into the second equation to find the value of y. Then, we can substitute the value of y back into the first equation to find the value of x.<br /><br />iii) Using the elimination method to solve the equations $2x+3y=4$ and $3x+2y=6$, we can multiply the first equation by 3 and the second equation by 2 to eliminate the y terms. Then, we can solve for x and substitute it back into one of the original equations to find the value of y.<br /><br />b. i) A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It can be used to represent and manipulate data in various fields such as mathematics, computer science, and engineering.