Question

which situation can be represented by this equation? 280 + 65x = 575. ① jeremy is traveling to a location that is 575 miles away. he has already traveled 280 miles. what is x, the number of hours that jeremy will need to travel at a speed of 65 miles per hour to reach the location? ② jeremy is traveling to a location that is 575 miles away. he has already traveled 280 miles. what is x, the number of additional miles that jeremy will need to travel to reach the location? ③ jeremy is reading a book with 575 pages. he has already read 65 pages and will read 280 pages per day. what is x, the number of days that jeremy will need to read to finish the book? ④ jeremy is reading a book with 575 pages. he has already read 315 pages. what is x, the number of pages jeremy has left to read to finish the book? m: per, each. b: initial, starting, added, fee. y: total. a relationship between x and y is shown on the graph. y = mx + b. m =, b =. complete the equation that best describes the relationship between x and y.

Explanation:

Step1: Analyze the equation structure

The equation is in the form \(y = mx + b\), where \(y\) is the total, \(m\) is the rate, \(x\) is the variable - quantity, and \(b\) is the initial amount. In the equation \(280+65x = 575\), \(280\) is the initial amount, \(65\) is the rate, and \(575\) is the total.

Step2: Evaluate each option

• Option 1: Jeremy is traveling to a location that is 575 miles away. He has already traveled 280 miles. The rate of 65 miles per hour means \(x\) is the number of hours he needs to travel at 65 miles per hour to reach the destination. The equation \(280 + 65x=575\) models this situation correctly as \(280\) (initial distance traveled) plus \(65x\) (distance traveled in \(x\) hours at 65 miles per hour) equals the total distance of 575 miles.
• Option 2: If \(x\) is the number of additional miles, the equation should be \(280+x = 575\), not \(280 + 65x=575\).
• Option 3: If Jeremy is reading a book with 575 pages, he has already read 65 pages and reads 280 pages per day, the equation should be \(65+280x = 575\), which is not the given equation.
• Option 4: If he has already read 315 pages of a 575 - page book, the equation for the number of pages left (\(x\)) is \(x=575 - 315\), not related to \(280 + 65x=575\).

Answer:

Jeremy is traveling to a location that is 575 miles away. He has already traveled 280 miles. What is \(x\), the number of hours that Jeremy will need to travel at a speed of 65 miles per hour to reach the location?