In this equation, find the value of $y$ when $x=-3$.
$y=\frac{4}{3} x+2$
Answer (1)
Substitute x = − 3 into the equation y = 3 4 x + 2 .
Calculate the product: 3 4 × − 3 = − 4 .
Add 2 to the result: − 4 + 2 = − 2 .
The value of y when x = − 3 is − 2 .
Explanation
Understanding the Problem We are given the equation y = 3 4 x + 2 and asked to find the value of y when x = − 3 . This is a straightforward substitution problem.
Substituting the Value of x To find the value of y , we substitute x = − 3 into the equation: y = 3 4 ( − 3 ) + 2
Calculating the Value of y Now, we simplify the expression: y = − 4 + 2 y = − 2
Examples
Understanding linear equations is crucial in many real-world applications. For instance, if you are tracking the cost of a taxi ride, the equation y = 3 4 x + 2 could represent the total fare ( y ) based on the number of miles traveled ( x ), where 3 4 is the cost per mile and 2 is the initial fee. By substituting different values of x , you can predict the cost of the ride for various distances. This concept extends to budgeting, where you can model expenses and savings using linear equations to forecast financial outcomes.
