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
Here are the steps to draw each straight line graph on a Cartesian Plane: Step 1: Analyze the first equation. The equation is y = 0. This equation represents all points where the y-coordinate is zero. This is the equation of the x-axis. To draw this line, simply draw a line that coincides with the x-axis. Step 2: Analyze the second equation. The equation is 4y - 2x = 4. To draw a straight line, we can find two points that lie on the line. A common method is to find the x-intercept (where y=0) and the y-intercept (where x=0). • To find the y-intercept, set x=0: 4y - 2(0) = 4 4y = 4 y = 1 This gives the point (0, 1). • To find the x-intercept, set y=0: 4(0) - 2x = 4 -2x = 4 x = -2 This gives the point (-2, 0). To draw the line, plot the points (0, 1) and (-2, 0) on the Cartesian plane and draw a straight line through them. The equation in slope-intercept form (y = mx + c) is: 4y = 2x + 4 y = (1)/(2)x + 1 The slope is (1)/(2) and the y-intercept is 1. Step 3: Analyze the third equation. The equation is 2x + 2y = 4. Again, we find the x-intercept and y-intercept. • To find the y-intercept, set x=0: 2(0) + 2y = 4 2y = 4 y = 2 This gives the point (0, 2). • To find the x-intercept, set y=0: 2x + 2(0) = 4 2x = 4 x = 2 This gives the point (2, 0). To draw the line, plot the points (0, 2) and (2, 0) on the Cartesian plane and draw a straight line through them. The equation in slope-intercept form (y = mx + c) is: 2y = -2x + 4 y = -x + 2 The slope is -1 and the y-intercept is 2. Summary of points for plotting: For y=0: The line is the x-axis*. For 4y - 2x = 4: Plot points (0, 1) and (-2, 0). For 2x + 2y = 4: Plot points (0, 2) and (2, 0). Send me the next one 📸