The line $y = b-x$ with $0 < b < 4$ intersects the $y$-axis at $p$ and the line $x=4$ at $s$. if the ratio of the area of triangle $qrs$ to the area of triangle $qop$ is 9: 25, what is the value of $b$? express the answer as a decimal to the nearest tenth.

b=2.5

Step-by-step explanation:

The given line has equation:

The x-intercept is (b,0)

The y-intercept is (0,b)

The area of triangle QOP

The area of triangle QRS

The area of triangle QRS and QOP are in the ratio 9:25

We must negate the area under the x-axis.

But 0<b<4

Therefore b=2.5

VERIFY

The area of triangle QOP

The area of triangle QRS

We must take absolute value because this area is below the x-axis.

ian gonna lie that is way to much