Which of the following could be the graph of 2(y+1)=-6(x-2)?
(A)
(B)
(C)
(E)
Answer (1)
Simplify the given equation 2 ( y + 1 ) = − 6 ( x − 2 ) .
Convert the simplified equation to slope-intercept form: y = − 3 x + 5 .
Identify the slope m = − 3 and y-intercept b = 5 .
Choose the graph that has a slope of -3 and a y-intercept of 5. The equation is y = − 3 x + 5 .
Explanation
Understanding the Problem We are given the equation 2 ( y + 1 ) = − 6 ( x − 2 ) and asked to determine which graph could represent this equation. To do this, we will simplify the equation and convert it to slope-intercept form, which is y = m x + b , where m is the slope and b is the y-intercept.
Distributing Constants First, distribute the constants on both sides of the equation: 2 y + 2 = − 6 x + 12
Isolating y Next, isolate y by subtracting 2 from both sides: 2 y = − 6 x + 10
Solving for y Now, divide both sides by 2 to solve for y :
y = − 3 x + 5
Identifying Slope and Y-intercept From the slope-intercept form y = − 3 x + 5 , we can see that the slope m = − 3 and the y-intercept b = 5 . We are looking for a graph with a negative slope and a y-intercept of 5.
Finding the Correct Graph By examining the provided options (which are not visible to me), we need to identify the graph that has a slope of -3 and intersects the y-axis at 5. Without the graphs, I cannot definitively choose the correct one. However, the process outlined above will allow you to select the correct graph.
Examples
Understanding linear equations and their graphical representations is crucial in various real-life scenarios. For instance, if you are tracking the depreciation of a car's value over time, you might use a linear equation to model the relationship between the car's age and its value. The slope would represent the rate of depreciation, and the y-intercept would represent the initial value of the car. By understanding the equation and its graph, you can predict the car's value at any point in time.
