The general equation of a line is:
![y=m\cdot x+b](https://img.qammunity.org/2023/formulas/mathematics/college/3vdit4cyikmz0crw73cnwv4b8bte4f6lad.png)
Where m is the slope of the line and b its the value of the y-intercept of the line.
Q) The question asks about the equation of a graphed line.
A) In order to find the equation of the line, we note that it passes through the points:
![\begin{gathered} (x_1,y_1)=(0,-2) \\ (x_2,y_2)=(4,-1) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/b2hn20ilt9o35mtq5p4k7htxeh8ifu9iyd.png)
The first point give us the value of the y-intercept of the line (b), so the y-intercept is y = -2, and we have:
![b=-2](https://img.qammunity.org/2023/formulas/mathematics/high-school/h6ex3l0mrsxxjxsc59x018wah3tawx95xl.png)
Now we must calculate the slope (m) of the line. In general the slope of a line is given by the following formula:
![m=(y_2-y_1)/(x_2-x_1)](https://img.qammunity.org/2023/formulas/mathematics/high-school/78uaqhwt0aws3qfwxigaftpihnmb1gzxtp.png)
Where (x1,y1) and (x2,y2) are the coordinates of two points of the line. Using the points of above and the last formula we find that:
![m=(y_2-y_1)/(x_2-x_1)=(-1-(-2))/(4-0)=(2-1)/(4)=(1)/(4)](https://img.qammunity.org/2023/formulas/mathematics/college/irndwbw82xp6yrldsbh0rytf0nagtkz8gu.png)
Answer
Using the values of m and b, and the general equation, we find that the equation of the line is:
![y=m\cdot x+b=(1)/(4)x-2](https://img.qammunity.org/2023/formulas/mathematics/college/g2kxilh4ar78s8upg5le5nzp0uf5wyrd3s.png)
Or: y = 1/4 x - 2
So the correct option is option number 3.