First you must know the standard equation of a line and this is expressed as:
[tex]y\text{ = mx+c}[/tex]where:
m is the slope of the line
c is the intercept
Given
Slope m = 5/2
Next is to get the intercept c:
To do that, you will substitute m = 5/2 and the coordinate (0, -4) into the equation above as shown:
[tex]\begin{gathered} -4\text{ = 5/2(0)+c} \\ -4\text{ = 0+c} \\ c\text{ = -4} \end{gathered}[/tex]Next is to get the required equation by substituting m = 5/2 and c = -4 into the equation above as shown:
[tex]\begin{gathered} y\text{ = mx + c} \\ y\text{ = }\frac{5}{2}x\text{ +(-4)} \\ y\text{ = }\frac{5}{2}x\text{ - 4} \end{gathered}[/tex]Hence the required equation is espressed as:
[tex]y\text{ = }\frac{5}{2}x-4[/tex]