Aisha and Carolina each sketch a graph of the linear equation y = -
•x + 2. Aisha uses the equation y =
4
4
a. Explain how this leads them to use different steps to construct their graphs.
b. Will the two graphs look the same? Explain.
x + 2 to sketch the graph, and Carolina uses the equation y =
- 4×+2.
a. Choose the correct answer below.
O A. When they use the slope to plot the second point, Aisha moves left 3 units and up 4 units while Carolina goes right 3 units and down 4 units.
B. Aisha identifies the y-intercept as 4, and Carolina identifies the y-intercept as — 4.
• C. When they use the slope to plot the second point, Aisha moves down 3 units and right 4 units while Carolina goes up 3 units and left 4 units.
a. Aisha uses the equation y = (4/4)x + 2 and Carolina uses the equation y = (-4/1)x + 2. The different steps they use to construct their graphs are based on the different slopes of the equations. Aisha's equation has a slope of 4/4, which simplifies to 1, so she moves 1 unit up and 1 unit to the right to plot the second point. Carolina's equation has a slope of -4/1, which simplifies to -4, so she moves 4 units down and 1 unit to the right to plot the second point.
b. The two graphs will not look the same because the slopes of their equations are different. Aisha's graph will have a positive slope of 1, meaning it will slope upward from left to right. Carolina's graph will have a negative slope of -4, meaning it will slope downward from left to right. Therefore, the direction and steepness of the lines will be different in each graph.