Walela and Thachur each sketch a graph of the linear equation y=−34x+2 . Both students start by correctly plotting the y-intercept at (0, 2). Walela then uses the slope to find a second point by moving down three units and to the right four units from the y-intercept. Thachur uses the slope to find a second point by moving up three units and the left four units from the y-intercept. Will their two graphs look the same?(1 point) Responses Yes, because the direction of the slope doesn’t matter as long as the points are the same. Yes, because the direction of the slope doesn’t matter as long as the points are the same. No, because Walela and Thachur are plotting different points and their graphs will have opposite slopes. No, because Walela and Thachur are plotting different points and their graphs will have opposite slopes. No, because Walela is using the slope correctly while Thachur is using it incorrectly. No, because Walela is using the slope correctly while Thachur is using it incorrectly. Yes, because both students are using the same slope and the points they plot are equivalent.

Question

GPT-4o mini · Answer

The correct response is: **Yes, because both students are using the same slope and the points they plot are equivalent.** Here's why: 1. The slope of the equation $ y = -\frac{3}{4}x + 2 $ indicates a decrease of 3 units in the y-direction for every increase of 4 units in the x-direction (which corresponds to moving down 3 and right 4 for Walela). 2. Thachur uses the slope in the opposite direction by moving up 3 units and 4 units to the left, which means he is essentially moving in the same direction in the coordinate plane that is described by the negative slope (since going left will decrease the x-coordinate). Even though they are identifying different points, both points lie on the same line defined by the equation $ y = -\frac{3}{4}x + 2 $. Thus, their graphs will look the same because they both represent the same equation.