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
To draw the straight lines on a Cartesian plane, we need to find at least two points for each line. For the first line: y = x + 1 This equation is in the slope-intercept form y = mx + c, where m is the slope and c is the y-intercept. Here, the slope m = 1 and the y-intercept c = 1. Step 1: Find two points for y = x + 1. • When x = 0: y = 0 + 1 y = 1 So, one point is (0, 1). • When x = 2: y = 2 + 1 y = 3 So, another point is (2, 3). For the second line: y - x = 2 Rearrange this equation into the slope-intercept form y = mx + c: y = x + 2 Here, the slope m = 1 and the y-intercept c = 2. Step 2: Find two points for y = x + 2. • When x = 0: y = 0 + 2 y = 2 So, one point is (0, 2). • When x = 2: y = 2 + 2 y = 4 So, another point is (2, 4). Step 3: Draw the Cartesian plane. Draw an x-axis (horizontal) and a y-axis (vertical) intersecting at the origin (0,0). Label the axes. Step 4: Plot the points and draw the lines. • For y = x + 1: Plot (0, 1) and (2, 3). Draw a straight line through these points and label it y = x + 1. • For y = x + 2: Plot (0, 2) and (2, 4). Draw a straight line through these points and label it y = x + 2. Note that both lines have the same slope (m=1), which means they are parallel to each other. 3 done, 2 left today. You're making progress.