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guajiro [1.7K]
3 years ago
14

A math teacher instructed students to graph the following equations on a coordinate plane. y=2.5x+2 and y=2x+4. If graphed corre

ctly at what points will the two lines intersect on the coordinate plane?
Mathematics
1 answer:
algol [13]3 years ago
8 0

Both the graphical lines will intersect at (4,12)

Step-by-step explanation:

Step 1; We must find the point in the graph where the lines of y=2.5x+2 and y=2x+4 intersect. To find out the intersecting point we must substitute values of x in both equations and see in which co-ordinate they are the same.

Step 2; We plot various values of x on the line governed by the equation y=2.5x+2

For a value of x=1 , y=2.5(1) + 2 = 4.5

For a value of x=2 , y=2.5(2) + 2 = 7

For a value of x= 3, y=2.5(3) + 2 = 9.5

For a value of x= 4, y=2.5(4) + 2 = 12

For a value of x= 5, y=2.5(5) + 2 = 14.5

Step 3; Now we also plot the values of x on the other line governed by y=2x+4

For a value of x= 1, y=2(1) + 4 = 6

For a value of x= 2, y=2(2) + 4 = 8

For a value of x= 3, y=2(3) + 4 = 10

For a value of x= 4, y=2(4) + 4 = 12

For a value of x= 5, y=2(5) + 4 = 14

Step 4; For both lines we must see if any of the values repeat at a particular point. In this case at the point (4,12) repeats for both so that becomes the point of intersection.

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For this question, you can use something called a box method and factor it by finding a factor of each column and row. Just make 4 boxes and put 5x² on the top left and -40 on the bottom left box. Put 2x on the top right box and -20x on the bottom left box. Now, factor out for each row and column. The factors should be 5x + 2 for the top part and x - 4 for the side. It should look like (5x + 2)(x - 4). Let's check it. Solve it by using the FOIL method and you get 5x² - 20x + 2x - 8. Combine like terms and you get 5x² - 18x - 8. There. The answer is B: (5x + 2)(x - 4)

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