Solution
From the given graph
To find the slope of a given line, we pick two points from the graph and use their x and y coordinates to find the slope as shown below
Where
[tex]\begin{gathered} x=0,y=-4 \\ (x_1,y_1)\Rightarrow(0,-4) \\ x=6,y=5 \\ (x_2,y_2)\Rightarrow(6,5) \end{gathered}[/tex]
To find the slope of a line, the formula is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the coordinates into the formula above
[tex]\begin{gathered} \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \frac{y-(-4)}{x-0}=\frac{5-(-4)}{6-0} \\ \frac{y+4}{x}=\frac{5+4}{6} \\ \frac{y+4}{x}=\frac{3}{2} \end{gathered}[/tex]
Crossmultiply
[tex]\begin{gathered} 2(y+4)=3(x) \\ 2y+8=3x \\ 2y=3-8 \\ Divide\text{ both sides by 2} \\ \frac{2y}{2}=\frac{3x-8}{2} \\ y=\frac{3}{2}x-4 \end{gathered}[/tex]
Hence, the equation of the given line in the slope-intercept form is
[tex]y=\frac{3}{2}x-4[/tex]
