Answer:
The system that is represented by the graph is (a) [tex]y=3x-2\\y=3x-1[/tex].
Step-by-step explanation:
The Slope-Intercept Form of the equation of a straight line is given by:
[tex]y = mx + b[/tex]
the slope is given by [tex]m[/tex] and the y-intercept is given by [tex]b[/tex].
The slope of a line is a number that measures its "steepness" and its given by:
[tex]Slope=m=\frac{\:change \:in \:y}{\:change \:in \:x}=\frac{y_2-y_1}{x_2-x_1}[/tex]
The y-intercept is where a line crosses the y-axis of a graph (0, b).
From the graph, we can see that the y-intercept is -1 for the blue line and -2 for the orange line.
The blue line appears to go through the points (0,-1) and (1, 2) and the slope is
[tex]m=\frac{2+1}{1-0}=\frac{3}{1}=3[/tex]
The orange line appears to go through the points (0,-2) and (1, 1) and the slope is
[tex]m=\frac{1+2}{1-0}=\frac{3}{1}=3[/tex]
So, the system that is represented by the graph is
[tex]y=3x-2\\y=3x-1[/tex]
