Answer: Graph (B) is correct. Image is attached below.
Step-by-step explanation: We are given to select the graph that has a slope of 1.
We know that
the slope of a graphed line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
For graph (A) :
the line passes through the points (0, 0) and (4, 1). So, the slope of the graphed line will be
[tex]m=\dfrac{1-0}{4-0}=\dfrac{1}{4}\neq 1.[/tex]
So, this option is incorrect.
For graph B :
the line passes through the points (0, 0) and (2, 2). So, the slope of the graphed line will be
[tex]m=\dfrac{2-0}{2-0}=\dfrac{2}{2}=1.[/tex]
So, this option is correct.
For graph C :
the line passes through the points (0, 0) and (2, 1). So, the slope of the graphed line will be
[tex]m=\dfrac{1-0}{2-0}=\dfrac{1}{2}\neq 1.[/tex]
So, this option is incorrect.
For graph D :
the line passes through the points (0, 0) and (20, 5). So, the slope of the graphed line will be
[tex]m=\dfrac{5-0}{20-0}=\dfrac{5}{20}=\dfrac{1}{4}\neq 1.[/tex]
So, this option is incorrect.
Thus, the graph (B), the top second one is the correct option. Its image ia attached below.
