What is the correct order of steps to change $4x + 2y = 14$ from standard form to slope-intercept form?
1. $2y = -4x + 14$ Rearrange so $x$ is first.
2. $4x + 2y = 14$ The original equation.
3. $2y = 14 - 4x$ Subtract $4x$ from both sides.
4. $y = -2x + 7$ Divide everything by?
Answer (1)
Start with the original equation: 4 x + 2 y = 14 .
Isolate the y term by subtracting 4 x from both sides: 2 y = − 4 x + 14 .
Divide both sides by 2 to solve for y : y = − 2 x + 7 .
The equation is now in slope-intercept form: y = − 2 x + 7 .
Explanation
Understanding the Problem We are given the equation in standard form: 4 x + 2 y = 14 . Our goal is to convert it into slope-intercept form, which is y = m x + b , where m represents the slope and b represents the y-intercept. We need to identify the correct order of steps to achieve this transformation.
Starting with the Original Equation The first step is to start with the original equation: 4 x + 2 y = 14
Isolating the y-term Next, we want to isolate the term with y . To do this, we subtract 4 x from both sides of the equation: 2 y = 14 − 4 x or, equivalently, 2 y = − 4 x + 14
Solving for y Finally, to solve for y , we divide both sides of the equation by 2: 2 2 y = 2 − 4 x + 14 y = − 2 x + 7
The Correct Order of Steps Therefore, the correct order of steps is:
4 x + 2 y = 14 (The original equation)
2 y = 14 − 4 x (Subtract 4 x from both sides, or equivalently 2 y = − 4 x + 14 )
y = − 2 x + 7 (Divide everything by 2)
Examples
Understanding how to convert linear equations from standard form to slope-intercept form is useful in many real-world scenarios. For example, if you are managing a budget where 'x' represents the number of hours worked and 'y' represents the amount of money saved, converting the budget equation to slope-intercept form allows you to easily see how much money is saved per hour worked (the slope) and the initial savings (the y-intercept). This helps in making informed decisions about work hours and savings goals. Another example is in physics, where you might have a relationship between distance and time in standard form, converting it to slope-intercept form immediately tells you the speed (slope) and initial position (y-intercept).
