Find the number of square units in the area of the triangle.
Let's start by remembering that a straight line can be represented by y = mx + b,
where m stands for the slope of the line and b stands for the y-intercept.
We have two points on the line so let's use those. First, determine m.
Δy (6) – (2) 4
m = ––– = –––––––––– = ––– = 1
Δx (–2) – (–6) 4
Now we're getting somewhere. Let's use one of those points to determine b.
y = mx + b
2 = (1)(–6) + b
2 = –6 + b
b = 8
So, the formula for the line is y = x + 8
So, when x is 0, y is 8
and when y is 0, x is –8.
That makes each leg of the triangle 8 units long.
And it's a right triangle because the origin is a right angle.
Therefore, we can calculate the area as A = (1/2)(Base)(Height)
A = (1/2)(8)(8)
A = 32 square units
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