[tex]m=5,\:b=-4[/tex]
1) Since we knw towo solutions for this function, we can set a system of linear equations to find the slope m and the y-intercept. Let's use the Substitution Method.
[tex]\begin{gathered} f(x)=y \\ y=mx+b \\ (6,26),(-5,-29) \\ 26=6x+b \\ -29=-5x+b \\ \begin{bmatrix}-6m-b=-26 \\ 5m-b=29\end{bmatrix} \\ \\ 26=6m+b\Rightarrow6m+b=26\Rightarrow\frac{6m}{6}=\frac{26}{6}-\frac{b}{6}\Rightarrow m=\frac{26-b}{6} \\ \\ Substitute: \\ -29=-5(\frac{26-b}{6})+b \\ -29=-\frac{130}{6}+\frac{5b}{6}+b \\ -29=-\frac{130}{6}+\frac{11}{6}b \\ -\frac{130}{6}+\frac{11}{6}b=-29 \\ -\frac{130}{6}+\frac{11}{6}b+\frac{130}{6}=-29+\frac{130}{6} \\ \frac{11}{6}b=-\frac{22}{3} \\ 6\cdot \frac{11}{6}b=6\left(-\frac{22}{3}\right) \\ 11b=-44 \\ b=-4 \end{gathered}[/tex]
Now that we know the quantity of b, let's plug into one of those equations and solve for x:
[tex]\begin{gathered} 6m+b=26 \\ 6m-4=26 \\ 6m=26+4 \\ 6m=30 \\ \frac{6m}{6}=\frac{30}{6} \\ m=5 \end{gathered}[/tex]
Thus, these are the answers m=5, b=-4
