Question 61·Easy·Linear Functions
The linear function is defined by . For what value of does ?
For linear function questions like this, always start by writing an equation: set the given function expression equal to the specified value (here, ). Then use basic inverse operations in order—undo subtraction or addition first, then undo multiplication or division—to isolate . Finally, quickly check by substituting your -value back into the original function to ensure it produces the required output, and match it to the corresponding choice.
Hints
Write the equation using the given function
You know . If , what equation can you write that involves and 18?
Use inverse operations step by step
Once you have the equation, think about how to get alone: what should you do first to remove the from ?
Finish isolating
After you remove the , you will have an equation of the form . What operation undoes multiplying by 5?
Desmos Guide
Graph the function
In Desmos, type y = 5x - 7 to graph the linear function .
Graph the constant value
On a new line, type y = 18 to graph a horizontal line representing .
Find the intersection
Click or tap on the point where the two lines intersect and read the -coordinate of that point; that -value is the solution to and matches one of the answer choices.
Step-by-step Explanation
Translate the function statement into an equation
You are told that and asked for the value of when .
Set the expression for equal to 18:
Isolate the term with
To solve for , first get rid of the by adding 7 to both sides of the equation:
Now the equation is simpler and only has in the term .
Solve for and match the answer choice
Now divide both sides by 5 to solve for :
So the value of that makes is , which corresponds to choice B) 5.