The line is a straight line, therefore, we can employ the equation of a line given 2 points form.
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]
We can pick any two points on the line,
I'll go with ( 0 , -1) and ( 5 ,5)
Inserting this into the equation, we can obtain;
[tex]\begin{gathered} \frac{5-(-1)}{5-0}=\frac{y-(-1)}{x-0} \\ \frac{6}{5}=\frac{y+1}{x} \\ 6x=5(y+1) \\ \text{Divide both sides by 5 to obtain} \\ \frac{6}{5}x=y+1 \\ y=\frac{6}{5}x-1 \end{gathered}[/tex]
As you can see, the line equation is y = (6/5)x - 1
The slope is 6/5 and the y-intercept is -1
