I'm assuming your teacher meant to say "line segment AB" and not "line segment AD". Point D is not given at all. If that assumption holds up, then you can proceed with the rest of the solution below. If not, then you'll have to talk to your teacher. I think its a typo but its possible that there's more context somewhere that I'm not seeing (a diagram maybe?)
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We're given the two points (2,7) and (5,1). The first thing we need to do is find the slope of the line through those points. Lets assign them to be equal to (x1,y1) and (x2,y2), so,
(x1,y1) = (2,7) and (x2,y2) = (5,1)
which further breaks down into these four items: x1=2 y1=7 x2=5 y2=1
Plug each of those into the slope formula and simplify m = (y2 - y1)/(x2 - x1) m = (1 - 7)/(5 - 2) m = (-6)/(3) m = -2
The slope is -2. We'll use this to find the y intercept. We'll also use one of the points given to us, say the point (2,7)
(x,y) = (2,7) ---> x = 2 and y = 7
Plug m = -2, x = 2, and y = 7 into the equation below and solve for b y = m*x + b 7 = -2*2 + b 7 = -4 + b 7 + 4 = -4 + b + 4 11 = b b = 11
So we figured out that m = -2 is the slope and b = 11 is the y intercept
Therefore, the equation y = mx+b turns into y = -2x+11
Final Answer: y = -2x+11
------------------------------------------------- Checking the answer: plug in x = 2 and we get... y = -2*x + 11 y = -2*2 + 11 y = -4 + 11 y = 7 so that proves (x,y) = (2,7) is on the line y = -2x+11
Plug in x = 5 and we get... y = -2*x + 11 y = -2*5 + 11 y = -10 + 11 y = 1 so that proves (x,y) = (5,1) is on the line y = -2x+11
Both points are on the same line y = -2x+11 so the answer is confirmed
A statement that follows with little or no proof required from an already proven statement. For example, it is a theorem<span> in geometry that the angles opposite two congruent sides of a triangle are also congruent. A </span>corollary<span> to that statement is that an equilateral triangle is also equiangular</span>
1) Yes because the two shorter lines combined are longer than the base and so those two lines are able to make a triangle.
2) No because the two lines on top will be equal to base line and so the two shorter lines will not be able to make a third angle because it will be level with the base.
Absolute value is the magnitude of a number without regard to its sign. for example, the absolute value of 5 is 5, and the absolute value of -5 is also 5!
