Pls pls pls graph 4x + 3y = 12

2 answers:

7 0

You have to start by converting the equation to slope intercept form, or $y=mx+b$ , where m represents the slope, and b represents the y-intercept. Start by subtracting 4x on both sides in order to move it to the other side of the equation. This gives us $3y=12-4x$ . Switch around 12 and -4x to conform to the formula; $3y=-4x+12$ . Finally, divide by 3 to isolate y; $y=-\frac{4}{3}x+4$ . This is the final equation, and it tells us two things, firstly that the slope is negative 4/3, which means that for every 4 units the line goes up, it goes left 3 units, and for every 4 units the line goes down, it goes right 3 units. The y-intercept is where the line intersects when x = 0. 4 is the y-intercept, as it intersects the line at (0, 4). You can then graph it on an online calculator or graph paper. For this example I used an online calculator called 'Desmos'.

madam [21]1 year ago

6 0

Answer:

Step-by-step explanation:

You might be interested in

Dont really understand how to do this

bija089 [108]

Answers:

$t_{10} = -22 \ \text{ and } S_{10} = -85$

========================================================

Explanation:

$t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2$

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

$t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4$

and so on. This process may take a while to reach $t_{10}$

There's a shortcut. The nth term of any arithmetic sequence is

$t_n = t_1+d(n-1)$

We plug in $t_1 = 5 \text{ and } d = -3$ and simplify

$t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8$

Then we can plug in various positive whole numbers for n to find the corresponding $t_n$ value. For example, plug in n = 2

$t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2$

which matches with the second term we found earlier. And,

$tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}$

---------------------

The notation $S_{10}$ refers to the sum of the first ten terms $t_1, t_2, \ldots, t_9, t_{10}$

We could use either the long way or the shortcut above to find all $t_1$ through $t_{10}$ . Then add those values up. Or we can take this shortcut below.

$Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}$