Explanation:
The points given in the question is given below as
[tex]\begin{gathered} (46,368)=(x_1.y_1) \\ (64,422)=(x_2,y_2 \end{gathered}[/tex]To figure out the equation of the line, we will use the formula below
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y-y_{1}}{x-x_{1}} \\ \frac{422-368}{64-46}=\frac{y-368}{x-46} \\ \frac{54}{18}=\frac{y-368}{x-46} \\ y-368=3(x-46) \\ y-368=3x-138 \\ y=3x-138+368 \\ y=3x+230 \end{gathered}[/tex]Hence,
The equation of the line in slope intercept form is
[tex]y=3x+230[/tex]Part B:
To figure out the number of calories for 52.4 grams, we will use the formula above
Put x=52.4
[tex]\begin{gathered} y=3x+230 \\ y=3(52.4)+230 \\ y=157.2+230 \\ y=387.2 \end{gathered}[/tex]Hence,
The number of calories for 52.4grams will be
[tex]387.2calories[/tex]Part C:
Hence,
From the slope above in part a
If the weight of the candy bar is increased by 1 gram ,the number of calories will increase by 3 calories