Answer:
Step-by-step explanation:
For the graphing, we can graph both equations, and where they intercept is the answer. Okay, so we can give x random inputs and get y as an output which is one pair of coordinates. I usually like using 0 as x. y-3(0)=12. y-0=12. y=12. So for our first equation, on of the coordinates is (0,12). Now we can insert another input for x! ( I chose 1.) y-3(1)=12. y-3=12. y=15. So our other pair of coordinates for the first equation is (1,15). We can do the same with the second equation. 2y+8(0)= -4. 2y+0= -4. y=-2. The first pair of coordinates for the second equation is (0,-2). Another input we can put in is 1, again. 2y+8(1)=-4. 2y+8=-4. 2y= -12. y= -6. So our second pair of coordinates for our second equation is (1,-6). We can graph this with a graphing calculator, or mark these points and draw a straight line through them. When we draw a line through them, the part where the two lines intersect is the answer.
When we do substitution, we need to solve for x or y in the bottom equation. I want to solve for x. ( NOTE: IF YOU SOLVE FOR y, YOU STILL GET THE SAME ANSWER) x=-56-3y. Then we replace the x on the top equation with 56-3y. And we get: 2(56-3y)-y=0. We can use the distributive property. The answer I have is 112-6y-y=0. -6y-y is -7y. 112-7y=0. We can add 7y to both sides so they seperate the variables and the numbers. 112=7y. Lastly, divide by 7. For y, we get 16. To get x, we insert y, AKA 16 into x+3y= -56. x+3(16)=-56. x+48= -56. Our last step to get x is to subtract 48 from both sides leaving us with: x= -100. Our final answer is y= 16 and x= -100.
Standard form : Ax + By = C
12y = 9x - 30
-9x + 12y = -30 ....some teachers accept this, with A being negative
but if not, then it is this :
9x - 12y = 30
Answer:
(4, - 5 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 270°
a point (x, y ) → (- y, x ) , thus
(- 5, - 4 ) → (4, - 5 )
Hello there! So, y = mx + b is in slope-intercept form, where m represents the slope, b represents the y-intercept, and y and x remain unfilled. First off, let's solve for the slope. The formula for slope is y2 - y1 / x2 - x1, where you subtract the first x and y coordinates from the second x and y coordinates. So it would be formed like this:
9 - 4 / 6 - (-4)
Let's subtract. 9 - 4 is 5. 6 - (-4) is 10. 5/10 is 1/2 in simplest form. The slope for this equation is 1/2. Now, let's find the y-intercept. We will find that by plugging one of the points into the equation and solving for b. The x and y coordinates will be filled in by that coordinate. Let's use (-4, 4) for this problem. We will also plug in the slope. In this case, the problem will look like this:
4 = (1/2)(-4) + b
Now, let's multiply 1/2 and -4 to get -2. Now, to get b by itself, subtract 2 to both sides to isolate the b. -2 + 2 cancels out. 4 + 2 is 6. b = 6. There. The equation of the line in slope-intercept form is y = 1/2x + 6.
Just divide it and you will get the answer
