Question

Nicholas has some cans at home to donate to the soup kitchen, but he decides to start a can drive at his school to see if other students will help. The table represents the number of cans donated, y, which is dependent on the number of days cans are collected, x.

A 2-column table with 3 rows. Column 1 is labeled x with entries 4, 7, 10. Column 2 is labeled y with entries 955, 1660, 2365.

Find the linear equation that represents the scenario.

Answer 1

A

Explanation:

Answer 2

y = 235x + 15

Explanation:

Equation of a Line

The equation of the line in slope-intercept form is:

y=mx+b

Where:

m = slope

b = y-intercept.

The point-slope form of the equation of a line is:

y - k = m ( x - h )

Where m is the slope and (h,k) is a point through which the line passes.

We are given 3 points and we must provide the equation of the line that passes through them all in slope-intercept form.

Selecting the points (4,955) and (7,1660) we can calculate the slope of the line by using the formula:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

`\displaystyle m=(1660-955)/(7-4)=(705)/(3)=235`

Now we use the point-slope equation with the first point (4,955):

y - 955 = 235 ( x - 4 )

Operating:

y - 955 = 235x - 940

y = 235x - 940 + 955

y = 235x + 15

The third point (10,2365) should pass through this line. To verify, substitute:

2365 = 235(10) + 15 = 2350 + 15= 2365

Since the identity is true, the equation is correct:

Answer:

y = 235x + 15