Answer :
ANSWER
[tex]\begin{gathered} a)m=4 \\ b)b=1 \\ c)y=4x+1 \end{gathered}[/tex]EXPLANATION
From the given graph;
To determine the slope, recall;
[tex]\begin{gathered} slope(m)=\frac{rise}{run}=\frac{\Delta y}{\Delta x} \\ =\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]a) Substitute the corresponding values of y and x from the graph,
Hence, slope m ;
[tex]\begin{gathered} x_1=1 \\ x_2=2 \\ y_1=1 \\ y_2=5 \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ =\frac{5-1}{2-1} \\ =\frac{4}{1} \\ =4 \end{gathered}[/tex]Given y=mx+b, b = y-intercept; the value of y where the graph intercepts the y-axis and from the graph, the y-intercept is;
[tex]b=1[/tex]c) The equation of the line after substituting the values is;
[tex]\begin{gathered} y=mx+b \\ m=4 \\ b=1 \\ y=4x+1 \end{gathered}[/tex]