Answer:
[tex]\frac{200}{3}[/tex] square units
Step-by-step explanation:
Knowing the function and that the triangle is formed by both the x and y-axis, you already have the triangle's height, which is 10 (the y-intercept of the functon) To find the base length, all you have to do is find the x-intercept. To do that, simply:
Set function equal to 0 and solve for x:
f(x) = 10 - [tex]\frac{3}{4}[/tex] x
0 = 10 - [tex]\frac{3}{4}[/tex] x
[tex]\frac{3}{4}[/tex] x = 10
x = [tex]\frac{40}{3}[/tex]
This means that the base length of the triangle is also [tex]\frac{40}{3}[/tex]. Now that you have the height and base length, you can
Plug values into the formula for the area of a triangle:
The area of a triangle is [tex]\frac{1}{2}[/tex] × height × base
Height = 10, base = [tex]\frac{40}{3}[/tex]
Area = [tex]\frac{1}{2}[/tex] × 10 × [tex]\frac{40}{3}[/tex]
Area = 5 × [tex]\frac{40}{3}[/tex]
Area = [tex]\frac{200}{3}[/tex]
