By rationalizing the denominator of
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The formula to find the slope of a line is m = 
where the x's and y's are your given coordinates and m is your slope. So, plug in your coordinates and solve.
m = <span>![\frac{y_2 - y_1}{x_2 - x_1} Plug in your coordinates m = [tex] \frac{-2 - 7}{8 - -1} Cancel out the double negative m = [tex] \frac{-2 - 7}{8 + 1} Simplify m = [tex] \frac{-9}{9} Divide m = -1 Now, plug that slope and one set of your given coordinates into point-slope form, [tex]y - y_1 = m(x - x_1)](https://tex.z-dn.net/?f=%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%20%20%20Plug%20in%20your%20coordinates%20%3C%2Fspan%3Em%20%3D%20%3Cspan%3E%5Btex%5D%20%5Cfrac%7B-2%20-%207%7D%7B8%20-%20-1%7D%20%20%20Cancel%20out%20the%20double%20negative%20%3C%2Fspan%3Em%20%3D%20%3Cspan%3E%5Btex%5D%20%5Cfrac%7B-2%20-%207%7D%7B8%20%2B%201%7D%20%20%20Simplify%20%3C%2Fspan%3Em%20%3D%20%3Cspan%3E%5Btex%5D%20%5Cfrac%7B-9%7D%7B9%7D%20%20%20Divide%20m%20%3D%20-1%20%20%3C%2Fspan%3E%20Now%2C%20plug%20that%20slope%20and%20one%20set%20of%20your%20given%20coordinates%20into%20point-slope%20form%2C%20%5Btex%5Dy%20-%20y_1%20%3D%20m%28x%20-%20x_1%29)
. I'll use (-1, 7).
<span>
Plug in your points and slope
</span>y - 7 = -1(x - -1) Cancel out the double negative
y - 7 = -1(x + 1) Use the Distributive Property
y - 7 = -x - 1 Add 7 to both sides
y = -x + 6 </span>
m = <span>
<span>
</span>y - 7 = -1(x - -1) Cancel out the double negative
y - 7 = -1(x + 1) Use the Distributive Property
y - 7 = -x - 1 Add 7 to both sides
y = -x + 6 </span>
Step-by-step explanation:
<u>YELLOW TRIANGLE:</u>
<u></u>
<u>PURPLE TRIANGLE:</u>
Since one of the angle is 45°, x = BC = 6
To prove:
<u>PINK TRIANGLE:</u>
<u></u>
The combined area of both gardens is 72 square meters.
Step-by-step explanation:
Given,
Width of John's garden = 9 meters
Width of Sarah's garden = 6 meters
Let,
l be the length of John's garden.
Length of John's garden = l+2
It is given that area of both gardens is same,
Area of Sarah's garden = Area of John's garden
Length * Width = Length * Width
Dividing both sides by 3
Length of John's garden = 4 meters
Length of Sarah's garden = 4+2 = 6 meters
Combined area = Area of John's + Area of Sarah's
Combined area = (Length * Width) + (Length * Width)
Combined area = (4*9)+(6*6)
Combines area = 36+36 = 72 square meters
The combined area of both gardens is 72 square meters.