$20 x-4 y=-36$
$y=[?] x+$
Answer (1)
Subtract 20 x from both sides of the equation: − 4 y = − 20 x − 36 .
Divide both sides by − 4 : y = 5 x + 9 .
Identify the slope and y-intercept: y = 5 x + 9 .
The equation in slope-intercept form is y = 5 x + 9 .
Explanation
Understanding the Problem We are given the equation 20 x − 4 y = − 36 and we want to rewrite it in the slope-intercept form, which is y = m x + b , where m is the slope and b is the y-intercept.
Isolating the y term First, we want to isolate the term with y . We can subtract 20 x from both sides of the equation: 20 x − 4 y − 20 x = − 36 − 20 x − 4 y = − 20 x − 36
Solving for y Next, we divide both sides of the equation by − 4 to solve for y :
− 4 − 4 y = − 4 − 20 x − 36 y = − 4 − 20 x + − 4 − 36 y = 5 x + 9
Identifying Slope and Intercept Now we have the equation in the form y = m x + b . Comparing this to our equation y = 5 x + 9 , we can see that m = 5 and b = 9 . Therefore, the equation in slope-intercept form is y = 5 x + 9 .
Examples
Understanding linear equations and slope-intercept form is crucial in many real-world applications. For example, if you are tracking the cost of a taxi ride, the initial fee could be the y-intercept and the cost per mile could be the slope. By understanding these concepts, you can easily predict the total cost of the ride based on the distance traveled. Similarly, in business, linear equations can model revenue and expenses, helping to forecast profits and make informed decisions.
