Lesson I haven't learned yet

Question

In my math class, we have a substitute. My math teacher left us with a worksheet with a topic that we haven't learned yet. Will you please explain to me how to do these? (please don't just give me the answers. I need to write out how I found it.)

I am in 8th-grade math. (not algebra)

Here are the questions:

1. x+y =-15 2. 2y + 8x = 1 3. 2x + y = 1 4. 3y - 2x = 9 5. 2y = -1x - 8

6) y - 4 = -3(x - 3) 7. .2 + 0.3y = 0.5 8. 1/4y + 3 = -5x 9. 3x +2y = -6 10. 3y = 2x + 15

11) y - 4x = 8 12. y - 8 = -1/2(x + 4) 13. 3x - 4y + 8 14. 6x - 2y + 10 15.8x - 4y = 20

16) 2x + 3y = 12 18..2x + y = -11 19. 0.8x + 0.4y = 1.2 20. 3y = 4x = 27

21) x - 4y = 8 22. y + 9 = 2(x + 5) 23. y - 1 = 2/3(x + 3)

Answer 1

16) 2x+3y=12

solve for y,

3y =-2x +12

divide by 3

y = (-2/3)x + 4 is the same equation but in slope intercept form

with the coefficient of the x term = the slope = -2/3

the y intercept = the constant term = 4 = the point (0,4)

the y intercept is the point where the line intersects the y axis

the x intercept is found by setting y=0 and solving for x

0=-2x/3 +4

2x/3 =4

x= 4(3/2) = 6 = the point (6,0)

the x intercept is where the line intersects the x or horizontal axis

it's also called a "zero"

plot the two intercepts and connect them with a straight line,

that's the graph of the equation.

about only thing else you could do is solve for x in terms of y

2x+3y=12

2x =12-3y

x = 6 -3y/2

or rewrite the equation in other forms, such as is done in 22) below

usually they just want you to solve for y in terms of x, which gives the slope and y intercept

and then graph it

22) y+9 = 2(x+5) this equation is in point slope form, with slope =2 = coefficient of the x term

and through the point (-5,-9)

general form of the point slope equation is y-k = m(x-h) where m=slope and (h,k) is the point the line goes through

you can rewrite it in slope intercept form, by solving for y

y = 2x+10-9

y =2x +1 where 2=slope and 1=y intercept = the point (0,1)

or

rewrite it in standard form, ax+by=c where a>0

2x-y =-1

or in general form: ax+by+c =0

2x-y+1 = 0

x intercept = (-1/2,0), as 2(-1/2) +0 +1 = 0

two intercepts are (0,1) and (-1/2,0) plot them and connect with a straight line

that's the graph of the original equation and the graph of each alternative form of the same equation