Complete the equation of the graphed linear function. Write the slope in decimal form. y=? x+?

y = 5/4x + 4

Complete the equation of the graphed linear function. Write the slope in decimal form.            

y=? x+?

\(\text{line } y = m\cdot x +b\)

1. slope ?

\(m = \frac{ \Delta y } {\Delta x} \\ m = \frac{4-0}{0-(-5)}\\ m=\frac{4}{5}\)

2. y - intersection ?

b = 4

\(y = m\cdot x +b \\ \boxed{~ y = \frac45 x+ 4 ~}\)

Proof:

if x = 0   =>   y = 4   okay

if y = 0   =>  \(\begin{array}{rcll} 0 &=& \frac45 x+ 4 \\ \frac45 x &=& -4 \\ x &=& -\frac54 \cdot 4\\ x &=& -5 \qquad \text{ okay } \end{array}\)