Please consider the attached graph.
We have been given that Ben is eating some pretzels and an entire small package of mustard as a snack. We are asked to find the equation that represents the relationship between the number of pretzels that Ben eats, x, and the total amount of sodium in his snack, y.
First of all, we will find the slope of the line using points (1,80) and (5,140).
[tex]m=\frac{140-80}{5-1}[/tex]
[tex]m=\frac{60}{4}[/tex]
[tex]m=15[/tex]
Now we will use point-slope form of equation [tex]y-y_1=m(x-x_1)[/tex], where m represents slope of line and point [tex](x_1,y_1)[/tex] is on the line.
We will substitute [tex]m=15[/tex] and coordinates of point (1,80) in above equation.
[tex]y-80=15(x-1)[/tex]
[tex]y-80=15x-15[/tex]
[tex]y-80+80=15x-15+80[/tex]
[tex]y=15x+65[/tex]
Therefore, the equation [tex]y=15x+65[/tex] represents the relationship between the number of pretzels that Ben eats and the total amount of sodium in his snack.
