An equivalent expression has the same value for every . The cue here is an expression made of multiples of and a constant, so it is linear. In Desmos, its value at gives the constant, and its change from to gives the number multiplying . Keep the minus sign inside the parentheses.
Hints
- Hint 1
A linear expression can be written as , where has no and multiplies . Which input makes every term containing disappear?
- Hint 2
At , equals . At , it equals . The difference between those outputs gives , the number multiplying . What would you type in Desmos to find it?
Step-by-step
Approach 1: Find both parts in Desmos
- Step 1
Find the constant
Call the given expression . It is linear: it has multiples of and a constant, so it fits . At , every term containing becomes . Type , then . Desmos shows , so the constant is negative.
- Step 2
Find the number multiplying x
For , moving from to changes the output by . Type ; Desmos shows , so is the coefficient multiplying . The value at and the change to determine a linear expression. With constant , the equivalent expression is . Choice D.
Approach 2: Distribute and combine by hand
- Step 1
Multiply both terms inside the parentheses
Use the distributive property: multiply by both terms, including the negative :
- Step 2
Combine the x terms
Add and to combine the like terms and . The has no , so it stays separate: . This is the equivalent expression. Choice D.