Final answer:
The question pertains to a linear relationship in which Joan adds 10 photos to her album each week. After 7 weeks, she has a total of 110 photos, indicating she had an initial 40 photos in the album. By solving the linear equation, we find that the increase in the number of photos each week is consistent.
Step-by-step explanation:
The question involves linear relationships in mathematics, where Joan adds a constant number of photos to her album each week. We are given that Joan plans to add 10 photos to her photo album each week and that after 7 weeks, there are 110 photos in the album. To confirm the relationship is linear, we simply multiply the number of weeks by the number of photos added per week (7 weeks × 10 photos/week) and add any initial number of photos already in the album at the start (if there were any).
If we let x represent the number of weeks and y the total number of photos in the album, the equation of the line would be y = 10x + b, where b is the initial number of photos. Knowing that y is 110 after 7 weeks, we can substitute these values into the equation to find b: 110 = (10 × 7) + b. This simplifies to 110 = 70 + b, and solving for b gives us b = 40.
Thus, the initial number of photos was 40, and the linear relationship is confirmed because the increase is steady with 10 photos added each week.