Question

Angela bought her dog Gizmo a bag of dog food. She feeds Gizmo the same amount of food every day. After 4 days, there was 11 pounds of food left in the bag. After 10 days, there was 6.5 pounds left in the bag. Write a linear equation (y = mx + b) to represent how much food was left in the bag as a function of the number of days.

Answer 1

To represent the amount of dog food left in the bag as a function of the number of days, we can use the linear equation y = -0.75x + 14.

Step-by-step explanation:

To write a linear equation representing the amount of dog food left in the bag as a function of the number of days, we can use the slope-intercept form y = mx + b. Let's assign the variable 'x' to the number of days and 'y' to the amount of food left in pounds. We are given two data points: (4, 11) and (10, 6.5). We can use these points to find the slope 'm' and the y-intercept 'b'. First, calculate the slope using the formula (y2 - y1) / (x2 - x1). We have (6.5 - 11) / (10 - 4) = -0.75. Now substitute one of the points and the calculated slope into the equation to find 'b'. We have 11 = (-0.75 * 4) + b. Solving for 'b', we get b = 14. Now we can write the linear equation as y = -0.75x + 14.