Write the equation in graphing form and the graph the shape. NO LINKS/ASSESSMENT!!
1 answer:
Answer:
see explanation
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Given
16 + x² + y² - 8x - 6y = 0 ( subtract 16 from both sides )
x² + y² - 8x - 6y = - 16 ( collect x and y terms together )
x² - 8x + y² - 6y = - 16
Use the method of completing the square
add ( half the coefficient of the x/y terms)² to both sides
x² + 2(- 4)x + 16 + y² + 2(- 3)y + 9 = - 16 + 16 + 9
(x - 4)² + (y - 3)² = 9 ← in standard form
with centre (4, 3 ) and r = = 3
This is a circle with centre (4, 3 ) and radius 3
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Answer:
Step-by-step explanation:
The equation of a line is y = mx + b
Where:
- m is the slope
- b is the y-intercept
First, let's find what m is, the slope of the line.
Let's call the first point you gave, (-3,1), point #1, so the x and y numbers given will be called x1 and y1.
Also, let's call the second point you gave, (2,-1), point #2, so the x and y numbers here will be called x2 and y2.
Now, just plug the numbers into the formula for m above, like this:
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
- (-3,1). When x of the line is -3, y of the line must be 1.
- (2,-1). When x of the line is 2, y of the line must be -1.
Now, look at our line's equation so far: .
is what we want, the -
is already set and x and y are just two 'free variables' sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-3,1) and (2,-1).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!
You can use either (x,y) point you want. The answer will be the same:
- (-3,1). y = mx + b or
, or solving for b:
.
.
- (2,-1). y = mx + b or
, or solving for b:
.
See! In both cases, we got the same value for b. And this completes our problem.
The equation of the line that passes through the points (-3,1) and (2,-1) is
We must find which of the following numbers has a value equal to -5:
To answer this question, we simplify each number:
Answer
The numbers that are equal to -5 are: