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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The slope is an expression of the change in y after a change in x.
Usually, this is expressed with a ratio, with the difference in y first.
The formula for slope is written as
.
Our points are
and 
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Of course, the difference is just subtracting one from the other, but you'll get either a positive or negative value depending on which way you subtract. That's all fine and dandy if you handle the differences in x and y in the same way like in the formula, because any unwanted negatives get cancelled out...it's not important.
Anyways, let's plug our points (2, 8) and (6, 12) into the slope formula.
Any number divided by 1 stays the same, so we can leave out the /1 and just have our slope be 1.
Usually, this is expressed with a ratio, with the difference in y first.
The formula for slope is written as
Our points are
Of course, the difference is just subtracting one from the other, but you'll get either a positive or negative value depending on which way you subtract. That's all fine and dandy if you handle the differences in x and y in the same way like in the formula, because any unwanted negatives get cancelled out...it's not important.
Anyways, let's plug our points (2, 8) and (6, 12) into the slope formula.
Any number divided by 1 stays the same, so we can leave out the /1 and just have our slope be 1.