Question Type 5: Finding values through substitution of values Exercises

For the line $y = mx + 5$, if it passes through $(2,11)$, find $m$.

For the model $y = a\cos(3x) + 9$, when $x = 0$ and $y = 11$, find the value of $a$.

Find $m$ and $b$ for the line $y = mx + b$ passing through $(1,3)$ and $(4,9)$.

For $y = 10e^{kx}$, if $y=20$ when $x = 1$, determine $k$.

Given $y=2x^2+bx+3$ passes through $(2,15)$, find $b$.

The model $y = 3a\sin(3x) + d$ passes through $(0,7)$ and $(\tfrac{\pi}{6},3)$. Determine $a$ and $d$.

For $p(x) = A\sin(Bx) + 2$, given $p(\tfrac{\pi}{2}) = 5$ and $p(\pi) = 2$, determine $A$ and $B$.

In the sinusoidal model $p(t) = P\cos(\omega t) + 3$, given $p(0)=8$ and $p(\tfrac{\pi}{2})=3$, find $P$ and $\omega$.

For $y = a\sin(4x) + 1$, if $y = 5$ when $x = \tfrac{\pi}{2}$, determine $a$.

In the exponential model $y = A e^{kx}$, suppose $y(0)=5$ and $y(2)=20$. Find $A$ and $k$.

Find $a,b,c$ if the quadratic $y = ax^2 + bx + c$ passes through $(1,4)$, $(2,9)$ and $(3,16)$.

Given $y = a\cos(2x) - 5$, and the point $(x,y)=(\tfrac{\pi}{4},3)$ lies on the curve, find $a$.