Answer:
[tex]\text{B. }\frac{1}{3}x-3=-x+1[/tex]
Step-by-step explanation:
Let's start by taking a look at the blue line. The slope of any line that passes through two points is equal to the change in y-values over the change in x-values. We can see that the line passes through points (0, 1) and (1, 0). Assign these points to [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex] (doesn't matter which you assign) and use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let:
[tex](x_1,y_1)\implies (0,1)\\(x_2,y_2)\implies (1, 0)[/tex]
The slope is equal to:
[tex]m=\frac{0-1}{1-0}=\frac{-1}{1}=-1[/tex]
Therefore, the slope of this line is -1. In slope-intercept form [tex]y=mx+b[/tex], [tex]m[/tex] represents slope, so one of the lines must have a term with [tex]-x[/tex] in it, which eliminates answer choices A and D.
For the second line, do the same thing. The red line clearly passes through (0, -3) and (3, -2). Therefore, let:
[tex](x_1,y_1)\implies (0,-3)\\(x_2,y_2)\implies (3, -2)[/tex]
Using the slope formula:
[tex]m=\frac{-2-(-3)}{3-0}=\frac{1}{3}[/tex]
Thus, the slope of the line is 1/3 and the other line must have a term with [tex]\frac{1}{3}x[/tex] in it, eliminating answer choice C and leaving the answer [tex]\boxed{\text{B. }\frac{1}{3}x-3=-x+1}[/tex]
*You can find the exact equation of each line by using the slope formula as shown and plugging in any point the line passes through into [tex]y=mx+b[/tex]
