Question

Show that the points $A\left(1,2\right)$, $B\left(-1,-16\right)$, and $C\left(0,-7\right)$ lie on the graph of the linear equation $y=9x-7$.

Answer 1

Proving that the points $A\left(1,2\right)$, $B\left(-1,-16\right)$, and $C\left(0,-7\right)$ lie on the graph of a linear equation.

The given equation is $y=9x-7$.

Substitute the $A\left(1,2\right)$, $B\left(-1,-16\right)$, and $C\left(0,-7\right)$ into the given equation.

Substitute$A\left(1,2\right)$ into the given equation.

$\begin{array}{rcl}y& =& 9x-7\\ 2& =& 9\left(1\right)-7\\ & \Rightarrow & 2=2\end{array}$

Substitute$B\left(-1,-16\right)$ into the given equation.

$\begin{array}{rcl}y& =& 9x-7\\ -16& =& 9\left(-1\right)-7\\ & \Rightarrow & -16=-16\end{array}$

Substitute $C\left(0,-7\right)$ into the given equation.

$\begin{array}{rcl}y& =& 9x-7\\ -7& =& 9\left(0\right)-7\\ & \Rightarrow & -7=-7\end{array}$

Observe that the points $A\left(1,2\right)$, $B\left(-1,-16\right)$, and $C\left(0,-7\right)$ satisfy the given equation.

Hence, the points $A\left(1,2\right)$, $B\left(-1,-16\right)$, and $C\left(0,-7\right)$ lie on the graph of given linear equation $y=9x-7$.