Question

Find a linear function g given g(-1/4) = -6 and g(2)=3, then find g(3)

Answer 1

hmmm let's take a look at say g(x)

\(\bf g(x)\iff y\) thus

one could say that \(\large {
\begin{array}{ccllll}
g\left(-\frac{1}{4}\right)&=&-6\\
g(x)&=&-6\\
g\left({\color{brown}{ x=-\frac{1}{4}}}\right)&=&-6\\
y&=&-6
\end{array}\implies x=-\frac{1}{4}\quad y=-6\implies \left(-\frac{1}{4},-6\right)
\\ \quad \\ \quad \\
\begin{array}{ccllll}
g\left(2\right)&=&3\\
g(x)&=&3\\
g\left({\color{brown}{ x=2}}\right)&=&3\\
y&=&3
\end{array}\implies x=2\quad y=-3\qquad \implies (2,3)
}\)

so.... what points does that line pass through?