This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey Ntokozo, good to see you again. To draw the graphs for the given linear equations, we will find two points for each line, typically the x-intercept and y-intercept, and then connect them. Step 1: Identify the first equation and its intercepts. The first equation is y = -x + 4. To find the y-intercept, set x = 0: y = -(0) + 4 = 4 So, the y-intercept is (0, 4). To find the x-intercept, set y = 0: 0 = -x + 4 x = 4 So, the x-intercept is (4, 0). Step 2: Identify the second equation and its intercepts. The second equation is y = -x - 4. To find the y-intercept, set x = 0: y = -(0) - 4 = -4 So, the y-intercept is (0, -4). To find the x-intercept, set y = 0: 0 = -x - 4 x = -4 So, the x-intercept is (-4, 0). Step 3: Describe how to draw the graphs. • For the first line, y = -x + 4: Plot the points (0, 4) and (4, 0) on a coordinate plane. Draw a straight line passing through these two points. This line has a slope of -1 and a y-intercept of 4. • For the second line, y = -x - 4: Plot the points (0, -4) and (-4, 0) on the same coordinate plane. Draw a straight line passing through these two points. This line also has a slope of -1 and a y-intercept of -4. Both lines are parallel because they have the same slope (m = -1). What's next? 📸