The first condition gives us a point that belongs to the line.
The second condition gives us the slope of the line.
If we write the line equation as:
[tex]f(x)=mx+b[/tex]we have that m has a value of 4/3 (m=4/3) as it is defined by the second condition.
Then, we can calculate the other unknown, the y-intercept "b", using the other condition:
[tex]\begin{gathered} f(-4)=(\frac{4}{3})\cdot(-4)+b=-10 \\ \frac{-16}{3}+b=-10 \\ b=-10+\frac{16}{3}=\frac{-30+16}{3}=\frac{-14}{3} \end{gathered}[/tex]Then, with a slope of 4/3 and an y-intercept of (-14/3), the linear function can be written as:
[tex]f(x)=\frac{-4}{3}x-\frac{14}{3}[/tex]