With even just two points, you can find the equation of a line in slope-intercept form.
Slope-intercept form: 
where 
is the slope and 
is the y-intercept
<u>1) Solve for the slope (</u><u>)</u>
The equation to solve for the slope is 
when the two points are 
and 
. Plug the coordinates of these points into the equation and solve for .
Then, plug into .
<u>1) Solve for the y-intercept (</u><u>)</u>
Then, take any of the given points and plug it into along with the slope. Isolate to get the y-intercept. Then, plug both m and b back into to get your final equation.
I hope this helps!
Answer:
√36 = 6
a^2 + b^2 = c^2
6^2 + 6^2 = c^2
36 + 36 = c^2
72 = c^2
√72 = c
2 36
2 18
2 9
3 3
6√2 = c
6√2 = (estimate rounded up, 8.49)
The given circles are given in standard form:
(x - xc)² + (y - yc)² = r²
The second quadrant is the one that has negative x coordinates and positive y coordinates.
This said, let's see all your options:
A) (x - 5)² + (y - 6)² = 25
xc = -(-5) = +5
yc = -(-6) = +6
C (5 , 6) is in the first quadrant.
B) (x + 1)² + (y - 7)² = 16
xc = -(+1) = -1
yc = -(-7) = +7
C (-1 , 7) is in the second quadrant.
C) (x - 4)² + (y + 3)² = 32
xc = -(-4) = +4
yc = -(+3) = -3
C (4, -3) is in the fourth quadrant.
<span>
D) (x + 2)² + (y - 5)²= 9</span>
xc = -(+2) = -2
yc = -(-5) = +5
C (-2 , +5) is in the second quadrant.
Therefore, the correct answers are B and D.
To find the equation of a line knowing two points it passes through, we must first find the slope and then substitute the x and y values to figure out the y intercept.
First thing is to find the slope using the formula m = Δy ÷ Δx
m = 5 - (-2) ÷ 4 - (-5)
Now we simplify
m = 7 ÷ 9
Our equation so far is y = 7/9x + b. Now we can substitute the values of x and y from a point to figure out the answer. The equation here uses the point (4,5)
5 = 7/9 · 4 + b
Get b on one side
5 - 28/9 = b
Simplify
b = 1 + 8/9
That makes the equation of the line y = 7/9x + (1 + 8/9)
Answer:
the area of the trapezoid is 32
Step-by-step explanation:
a (base)2
b (Base)6
h (height)8
