Question

Write the ecuación of the line in fully simplifica slope-intercept from

Answer 1

The line is a straight line, therefore, we can employ the equation of a line given 2 points form.

`(y_2-y_1)/(x_2-x_1)=(y-y_1)/(x-x_1)`

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;

`\begin{gathered} (5-(-1))/(5-0)=(y-(-1))/(x-0) \\ (6)/(5)=(y+1)/(x) \\ 6x=5(y+1) \\ \text{Divide both sides by 5 to obtain} \\ (6)/(5)x=y+1 \\ y=(6)/(5)x-1 \end{gathered}`

As you can see, the line equation is y = (6/5)x - 1

The slope is 6/5 and the y-intercept is -1