I am stuck on solving these 4 problems below. please help. I have tried but I ha

Question

I am stuck on solving these 4 problems below. please help. I have tried but I have stopped bcause I am not sure of what steps to take. I know i'm suppose to bring all the x's to one side and then solve frm there. it has to be in the form of y=mx+b in order to find the ordered pairs.

For each of the equations below create a table of 5 ordered pairs and, using any two of these pairs, calculate the ratio of the change in y to the change in x.

7. 2y + 5x = 9

8. 3(2x –4) + 3y = 3x

9. 2x + 3y = 2y – 7x

10. y = x

Explanation / Answer

First things first, we need to get these equations in the standard form of a line.

7. 2y + 5x = 9 -> (subtract 5x)
    2y = -5x + 9 -> (need to get y alone, so we divide everything by 2)
    y = -5/2(x) + 9/2 (standard form: y = mx + b)

8. 3(2x –4) + 3y = 3x (need to distrbute the 3)

    6x - 12 + 3y = 3x (now we get the y variable alone, subtracting 6x and adding 12 since 12 is negative)

    3y = -3x + 12 (clear the constant, which is 3 here, from y)

    y = -x + 4 (standard form: y = mx + b)

9. 2x + 3y = 2y – 7x (lets first get the x's to one side of the equals sign)

    3y = 2y - 9x (now we move the y's)

    y = -9x (standard form: y = mx + b We have no "b" for this equation, but that's OK. The b constant, aka Y-intercept, isn't always needed.)

10. y = x (This is already in standard form. Since m = slope and is in front of the x with the standard equation of a line, it is assumed that m = 1. This is because anytime you multiply anything by 1, you get the multiplying constant back for an answer, in this case, x.)

To make your tables, simply pick a value for x and solve for y. These create your 5 ordered pairs that you need to calculate slope.

One final note about slope, it is also called rate of change. A well writen explanation concerning this topic can be found at this website: http://www.regentsprep.org/regents/math/algebra/AC1/Rate.htm

Hope this helps!

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