The line L crosses the x-axis at (-8,0), and the y-axis, forming a triangle of area 16. What is the slope of the line?
+14905 What is the slope of the line?
Hello Guest!
If the area of the triangle is 16, the line must intersect the y-axis at 4, because 8*4/2=16.
The slope of the line it 4 : 8 = 0.5
!
+113 The length from the orign to A(8,0) is 8. The formula for the area of a trangle is Area = 1/2 x a x b.
Let the length from the orign to (8,0) be a. To find b we can set 16 = 1/2 x 8 x b, or 16 = 4 x b. So b = 16/4 = 4.
So the length from the orign, along the y-axis to B must be 4, giving us the coordinate B(0,4).
To calculate the slope of a line from A to B we subtract the coordinates of the y-components and divide these by
the diffrence between the coordinates of the x-components, so slope = \(\frac{B_y - A_y}{B_x-A_x} = \frac{4 - 0}{0-8} = \frac{4}{-8} = -\frac{1}{2} = -0.5\)
