Answer:
[tex]y = \frac{4}{3} x + 1[/tex] which is option d
Explanation:
The general form of the linear equation is:
y = mx + c
where:
m is the slope
c is the y-intercept
1- getting the slope:
To get the slope, we need to have two points that belong to the line.
From the graph, we can get the following points:
(0,1) and (1.5,3)
The slope can be calculated as follows:
[tex]slope (m) = \frac{y2-y1}{x2-x1} = \frac{3-1}{1.5-0} = \frac{4}{3} [/tex]
Therefore, the equation of the line now is:
[tex]y = \frac{4}{3} x + c[/tex]
2- getting the y-intercept:
To get the y-intercept, we will simply use a point that belongs to the line, substitute in the equation and solve for c. I will use the point (0,1) as follows:
[tex]y = \frac{4}{3} x + c[/tex]
1 = (4/3)(0) + c
c = 1
Based on the above, the equation of the line given is:
[tex]y = \frac{4}{3} x + 1[/tex]
Hope this helps :)
