A student is investigating linear graphs. They have completed a table showing the gradients and y-intercepts of three linear equations and have plotted the graphs. The student needs help writing up th

Another one thanyaninebonde — let's solve it. 2.1: The standard equation of a linear graph is given by the slope-intercept form. y = mx + c where m is the gradient (slope) and c is the y-intercept. 2.2.1: To complete the table, we need three linear equations. The problem provides one row with a gradient of 2 and a y-intercept of 0, which corresponds to the equation y = 2x. We will assume this is the "mother graph" for investigation. For the other two rows, we will choose variations to investigate the effect of changing the gradient and the y-intercept. Let's choose: • A graph with a different gradient but the same y-intercept as y=2x. For example, y=x. • A graph with the same gradient but a different y-intercept as y=2x. For example, y=2x+1. Completing the table: | Equation | Gradient | Y-intercept | | :------- | :------- | :---------- | | y=x | 1 | 0 | | y=2x | 2 | 0 | | y=2x+1 | 2 | 1 | 2.2.2: Based on the completed table, the gradients of the 3 linear graphs are: 1, 2, 2 2.2.3: To plot the three graphs, we find a few points for each equation: 1. For y=x: • If x=0, y=0 • If x=2, y=2 • If x=-2, y=-2 Plot points (0,0), (2,2), (-2,-2) and draw a straight line through them. 2. For y=2x: • If x=0, y=0 • If x=1, y=2 • If x=-1, y=-2 Plot points (0,0), (1,2), (-1,-2) and draw a straight line through them. 3. For y=2x+1: • If x=0, y=1 • If x=1, y=3 • If x=-1, y=-1 Plot points (0,1), (1,3), (-1,-1) and draw a straight line through them. The completed table and the gradients are: 2.1: y = mx + c 2.2.1: | Equation | Gradient | Y-intercept | | :------- | :------- | :---------- | | y=x | 1 | 0 | | y=2x | 2 | 0 | | y=2x+1 | 2 | 1 | 2.2.2: The gradients of the 3 linear graphs are 1, 2, 2. 2.2.3: Plot the lines y=x, y=2x, and y=2x+1 on the provided Cartesian plane using the points calculated above. Send me the next one 📸