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?

Guest Aug 2, 2022

#1**+1 **

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

!

asinus Aug 2, 2022

#2**+1 **

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 = \(\frac{B_y - A_y}{B_x-A_x} = \frac{4 - 0}{0-8} = \frac{4}{-8} = -\frac{1}{2} = -0.5\)

tuffla2022 Aug 3, 2022

edited by
tuffla2022
Aug 3, 2022

edited by tuffla2022 Aug 3, 2022

edited by tuffla2022 Aug 3, 2022

edited by tuffla2022 Aug 3, 2022

edited by tuffla2022 Aug 3, 2022

edited by tuffla2022 Aug 3, 2022

edited by tuffla2022 Aug 3, 2022