Answer:
Graph represented by 2nd option is the correct choice.
Step-by-step explanation:
Please find the attachment.
We have been provided a diagram and we asked to choose the graph that represents the increase in temperature by 4 degrees every hour.
Since temperature is increasing 4 degrees every hour, so the graph representing increase in temperature will have a line with a positive slope of 4.
We can see that the graphs represented in option 3 and 4 have a negative slope, so these options are not right choices.
Now let us find slope of lines represented in option 1 and 2 using slope formula.
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex], where,
[tex]y_2-y_1[/tex] = Difference between two y-coordinates.
[tex]x_2-x_1[/tex] = Difference between corresponding x-coordinates of same y-coordinates.
Now let us substitute coordinates of points (0,5) and (5,35) to find slope of 1st graph.
[tex]\text{Slope of 1st graph}=\frac{35-5}{5-0}[/tex]
[tex]\text{Slope of 1st graph}=\frac{30}{5}[/tex]
[tex]\text{Slope of 1st graph}=6[/tex]
Since the slope of line represented in 1st graph is 6. This means that temperature is increasing 4 degrees per hour, therefore, 1st option is not a correct choice.
Let us substitute coordinates of points (0,3) and (6,27) to find slope of 2nd graph.
[tex]\text{Slope of 2nd graph}=\frac{27-3}{6-0}[/tex]
[tex]\text{Slope of 2nd graph}=\frac{24}{6}[/tex]
[tex]\text{Slope of 2nd graph}=4[/tex]
Since the slope of line represented in 2nd graph is 4, which represents that temperature is increasing 4 degrees per hour, therefore, 2nd option is the correct choice.
