Final answer:
To graph the pair of linear equations 2x + y = 4 and 2x - y = 4, convert them to slope-intercept form and plot the graph. The vertices of the triangle formed by these lines and the y-axis are (0, 4), (0, -4), and (0, 0). The area of this triangle is 8 square units.
Step-by-step explanation:
To graph the pair of linear equations 2x + y = 4 and 2x - y = 4, we can start by converting them to slope-intercept form. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
- For the equation 2x + y = 4, subtract 2x from both sides to isolate y: y = -2x + 4.
- For the equation 2x - y = 4, subtract 2x from both sides and multiply by -1 to isolate y: y = 2x - 4.
Now we can plot the graph by choosing some x-values, plugging them into the equations to find the corresponding y-values, and then plotting the points.
The vertices of the triangle formed by these lines and the y-axis are (0, 4), (0, -4), and (0, 0). To find the area of this triangle, we can use the formula: Area = 1/2 * base * height.
The base of the triangle is the y-axis, which has a length of 4 units. The height is the distance between the y-axis and the line 2x - y = 4. We can find this distance by calculating the y-intercept of the line, which is -4, and taking the absolute value. Therefore, the area of the triangle is: Area = 1/2 * 4 * |-4| = 8 square units.
Learn more about Graphing linear equations