Use point-slope form.
But first let's find the slope.
(4, 2), (2, 4)
m = y2-y1/x2-x1
m = (4 - 2)/(2 - 4)
m = 2/-2
m = -1
So this is the slope, now we can plug this into the equation along with any point.
y - y1 = m(x - x1)
Where y1 is the y-value of the point, x1 is the x-value, and 'm' is the slope.
Let's plug in point (4, 2):
y - 2 = -1(x - 4)
This can be one of your options.
Distribute -1:
y - 2 = -x + 4
Add 2 to both sides:
y = -x + 6
This can be another of your options.
Add 'x' to both sides:
x + y = 6
This can be another of your options.
Solve for x:x/5 - 2 = x/2 + 3
Put each term in x/5 - 2 over the common denominator 5: x/5 - 2 = x/5 - (10)/5:x/5 - (10)/5 = x/2 + 3
x/5 - (10)/5 = (x - 10)/5:(x - 10)/5 = x/2 + 3
Put each term in x/2 + 3 over the common denominator 2: x/2 + 3 = x/2 + 6/2:(x - 10)/5 = x/2 + 6/2
x/2 + 6/2 = (x + 6)/2:(x - 10)/5 = (x + 6)/2
Multiply both sides by 10:(10 (x - 10))/5 = (10 (x + 6))/2
10/5 = (5×2)/5 = 2:2 (x - 10) = (10 (x + 6))/2
10/2 = (2×5)/2 = 5:2 (x - 10) = 5 (x + 6)
Expand out terms of the left hand side:2 x - 20 = 5 (x + 6)
Expand out terms of the right hand side:2 x - 20 = 5 x + 30
Subtract 5 x from both sides:(2 x - 5 x) - 20 = (5 x - 5 x) + 30
2 x - 5 x = -3 x:-3 x - 20 = (5 x - 5 x) + 30
5 x - 5 x = 0:-3 x - 20 = 30
Add 20 to both sides:(20 - 20) - 3 x = 20 + 30
20 - 20 = 0:-3 x = 30 + 20
30 + 20 = 50:-3 x = 50
Divide both sides of -3 x = 50 by -3:(-3 x)/(-3) = 50/(-3)
(-3)/(-3) = 1:x = 50/(-3)
Multiply numerator and denominator of 50/(-3) by -1:Answer: x = (-50)/3
The properties that apply true are:
1–as it implies the Pythagorean theorem; a^2+b^2=c^2
3–as it implies the basic rules of visualized geometry.
4–as the greater side(hypotenuse) is opposite the right angle.
NOT 2, as the accrue angles ARE complimentary.
Height of a trapezoid:
h = 5 · sin 80° = 5 · 0.985 = 4.924
x = 5 · cos 80° = 5 · 0.17365 = 0.868
7 - x = 7 - 0.868 = 6.132
By the Pythagorean theorem:
d² = 6.132² + 4.924²
d² = 37.6 + 24.25
d² = 61.85
d = √61.85
d = 7.86 ≈ 8
Answer: The length of a diagonal brace is 8 feet.
I know that this is an old question, but I'll add my input for future reference. The graph shown above is B) This is a function (as it passes the vertical line test), but it is NOT a one-to-one, as it fails the horizontal line test.
