The given point: (-6, 4)
slope of the line = 5/2
To get the equation of line in slope -intereot form, we will use the formula:
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}[/tex]Since we already know the slope, we need to find the y-intercept
point (-6, 4): x = -6, y = 4
We will substitute the slope and the point in the formula above to get y-intercept:
[tex]\begin{gathered} y\text{ = mx + b} \\ 4\text{ = }\frac{5}{2}(-6)\text{ + b} \\ 4\text{ = -15 + b} \\ 4\text{ + 15 = b} \\ b\text{ = 19} \end{gathered}[/tex]The equation of line in slope intercept becomes:
[tex]y\text{ = }\frac{5}{2}x\text{ + 19}[/tex]