Graph the equation in the standard window and in the given window. Determine which window better shows the shape of the graph and the x- and y- intercepts:
y= -2x + 24
[-15,15, -10,30] Xscl =3 Yscl =5
To graph the equation y = -2x + 24 in the standard window and the given window, follow these steps:
1. Standard window:
In the standard window, the x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10. The x-scale (Xscl) and the y-scale (Yscl) are set at the default values of 1.
To graph the equation in the standard window:
a. Plot the y-intercept: Set x = 0, so y = -2(0) + 24 = 24. Plot the point (0, 24).
b. Determine the x-intercept: Set y = 0, so 0 = -2x + 24. Solve for x: -2x + 24 = 0. Subtract 24 from both sides: -2x = -24. Divide by -2: x = 12. Plot the point (12, 0).
c. Connect the points to form a straight line.
d. Depending on your calculator or graphing tool, you can adjust the settings to change the line's thickness or style.
2. Given window:
In the given window, the x-axis ranges from -15 to 15, and the y-axis ranges from -10 to 30. The x-scale (Xscl) is set to 3, and the y-scale (Yscl) is set to 5.
To graph the equation in the given window:
a. Use the same steps as in the standard window to find the y-intercept (0, 24) and the x-intercept (12, 0).
b. Plot these points on a graph with the given window settings.
c. Connect the points to form a straight line.
To determine which window better shows the shape of the graph and the intercepts:
Compare the two graphs. Analyze which one makes the slope (-2) and the intercepts more clearly visible. Look for any distortion or compression of the line in either graph due to the chosen window settings.
In this case, since the given window is wider and allows for a larger x-axis and y-axis range, it is expected to display the shape of the line and the intercepts more accurately compared to the standard window. Thus, the given window is likely to better show the shape of the graph and the x- and y-intercepts.
To graph the equation y = -2x + 24, we will graph it in both the standard window and the given window.
Standard Window:
The standard window typically ranges from -10 to 10 on the x-axis and -10 to 10 on the y-axis. Let's start by graphing the equation in the standard window.
First, we'll find the x- and y-intercepts:
To find the x-intercept, set y = 0 and solve for x:
0 = -2x + 24
2x = 24
x = 12
So the x-intercept is (12, 0).
To find the y-intercept, set x = 0 and solve for y:
y = -2(0) + 24
y = 24
So the y-intercept is (0, 24).
Now, using these intercepts, we can plot the graph in the standard window:
- Graph the x-intercept (12, 0).
- Graph the y-intercept (0, 24).
- Connect the points with a straight line.
Given Window:
The given window ranges from -15 to 15 on the x-axis and -10 to 30 on the y-axis. Let's graph the equation in this window.
To make it easier, let's find some additional points:
When x = -15:
y = -2(-15) + 24
y = 30 + 24
y = 54
So, we have a point (-15, 54).
When x = 15:
y = -2(15) + 24
y = -30 + 24
y = -6
So, we have a point (15, -6).
Using these additional points, we can plot the graph in the given window:
- Graph the x-intercept (12, 0).
- Graph the y-intercept (0, 24).
- Graph the point (-15, 54).
- Graph the point (15, -6).
- Connect all the points with a straight line.
Determining the Best Window:
Comparing the two graphs, we can see that the given window better shows the shape of the graph and includes all the important information such as the x- and y-intercepts.
Hence, the given window [-15, 15, -10, 30] with the Xscl = 3 and Yscl = 5 is better for displaying the graph of the equation y = -2x + 24.