Can someone help with Quadratic Graphs please?

Algebra graphing help please!! Trying to put equations into graph ASAP?

• Hi, can someone help me with this? Could someone please explain to me in words (or if it includes more maths can u please show working out so I understand) how to put these into a "graph". I know the first part (a) of the question, but i don't know what i'd need to do to put them into a graph. (BTW: the x's are algebra x's not multiplying x's) Thanks :D Here is the actual question how it is worded in the exam: John bought 3 shirts and 4 pairs of socks for $78. Joan bought 2 shirts and 6 pairs of socks for $72. (a) Letting $x equal the price of a shirt and $y equal the price of a pair of socks, write an equation to represent each transaction. (I KNow this would be 3x+4y=78 and 2x+6y=72) (b) Draw the graphs of the two equations on the same set of x and y axes. (I don't know how to do this part. Apparently, x needs to end up being equal to 18 and y needs to end up being equal to 6, but i don't know how i would use graphing to do this? Do you need to include more maths equations or something?) (c) Read off the coordinates of the point of intersection (ie. where the two linse cross) to find the values of x and y. Can someone please tell me how i would go about doing this? Thanks so much for any help :)

• Answer:

  These are linear equations. The graph of each one is a straight line. Any point on the line has coordinate values that would satisfy the equation. Focus on one equation at a time. Since the graph is a line, all we need are two points with coordinates that satisfy the equation. The line that passes through them is the graph of the equation. For any particular equation, it will be the same line no matter which points we find. The easiest points to find are often the x- and y-intercepts: Find the value of one variable when the other is assumed to be zero. Here's how it works for your two equations: 3x + 4y = 78 If y=0, x=78/3 = 26, so the x-intercept is the point (26,0). If x=0, y=78/4 = 19.5, so the y-intercept is the point (0,19.5). If you'd rather get another point with integer coordinates, try using x=2 instead: If x=2, y = (78-6)/4 = 72/4 = 18, so the point (2,18) is on this line. 2x + 6y = 72 If y=0, x=72/2 = 36, so the x-intercept is the point (36,0). If x=0, y=72/6 = 12, so the y-intercept is the point (0,12). For each line, mark two points and draw the line that goes through both, and you'll have your graph. Part (c): The two lines cross at one point. It's the only point that's on both lines, and therefore its coordinates are the only common solution to the two equations. You should find that the lines intersect at (18,6), representing the solution x=$18 is the price of a shirt, and y=$6 is the price of a pair of socks.