For #4-6, use the equation [tex]y=-3 x+2[/tex] to find the value of [tex]y[/tex] at the given [tex]x[/tex] values.
#4. [tex]x=3[/tex]
#5. [tex]x=-\frac{5}{3}[/tex]
#6. [tex]x=0[/tex]
Answer (2)
Substitute x = 3 into y = − 3 x + 2 to find y = − 3 ( 3 ) + 2 = − 7 .
Substitute x = − 3 5 into y = − 3 x + 2 to find y = − 3 ( − 3 5 ) + 2 = 7 .
Substitute x = 0 into y = − 3 x + 2 to find y = − 3 ( 0 ) + 2 = 2 .
Substitute x = − 4 into y = − 3 x + 2 to find y = − 3 ( − 4 ) + 2 = 14 .
Therefore, the values of y are − 7 , 7 , 2 , 14 .
Explanation
Understanding the problem We are given the equation y = − 3 x + 2 and asked to find the value of y for different values of x . We will substitute each given x value into the equation to find the corresponding y value.
Calculating y for x=3 For x = 3 , we substitute into the equation: y = − 3 ( 3 ) + 2 = − 9 + 2 = − 7
Calculating y for x=-5/3 For x = − 3 5 , we substitute into the equation: y = − 3 ( − 3 5 ) + 2 = 5 + 2 = 7
Calculating y for x=0 For x = 0 , we substitute into the equation: y = − 3 ( 0 ) + 2 = 0 + 2 = 2
Calculating y for x=-4 For x = − 4 , we substitute into the equation: y = − 3 ( − 4 ) + 2 = 12 + 2 = 14
Final Answer Therefore, the values of y for the given x values are: When x = 3 , y = − 7 .
When x = − 3 5 , y = 7 .
When x = 0 , y = 2 .
When x = − 4 , y = 14 .
Examples
Understanding linear equations like y = − 3 x + 2 is crucial in many real-world scenarios. For instance, imagine a taxi service charges a flat fee of $2 and an additional 3 f ore v ery mi l e t r a v e l e d . Here , y re p rese n t s t h e t o t a l cos t , an d x re p rese n t s t h e n u mb ero f mi l es . B ys u b s t i t u t in g d i ff ere n t v a l u eso f x$, you can easily calculate the total fare for various distances. This simple equation helps in budgeting, understanding pricing models, and making informed decisions in everyday situations.
To find the values of y for given x values using the equation y = − 3 x + 2 : when x = 3 , y = − 7 ; when x = − 3 5 , y = 7 ; and when x = 0 , y = 2 .
;
