Answer:
[tex]y=2.5x[/tex]
Step-by-step explanation:
We have been given a graph that shows numbers of servings (y) in different amounts (x) of frozen yogurt listed on a carton.
To write an equation that gives the number of servings y in x pints, we will have to find the slope (rate of change) of our given linear function.
Since we know that rate of change of a function can be found by vertical change of the function divided by horizontal change of the function.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
m= Slope (rate of change).
[tex]y_2-y_1[/tex]=Difference between two y-coordinates.
[tex]x_2-x_1[/tex]=Difference between corresponding x-coordinates of the y-coordinates.
Upon substituting coordinates of two points (0,0) and (4,10) in slope formula we will get,
[tex]m=\frac{10-0}{4-0}[/tex]
[tex]m=\frac{10}{4}[/tex]
[tex]m=2.5[/tex]
The slope of our given line is 2.5.
Now we will write equation of our given line is slope-intercept form. The equation of a line in slope-intercept form is: [tex]y=mx+b[/tex], where m=slope and b = y-intercept (initial value).
Upon substituting m=2.5 and coordinates of point (4,10) in slope-intercept form of equation we will get,
[tex]10=2.5\times 4+b[/tex]
[tex]10=10+b[/tex]
[tex]10-10=b[/tex]
[tex]0=b[/tex]
Upon substituting m=2.5 and b=0 in slope-intercept form of equation we will get,
[tex]y=2.5x+0[/tex]
[tex]y=2.5x[/tex]
Therefore, the equation [tex]y=2.5x[/tex] will give the number of servings y in x pints.
