Mia records the distance traveled in x minutes in the table below, while Alexa uses a graph to record her distance traveled over the same time period. (look at the graphs)Based on the data on the graph and in the table, which statement gives an accurate comparison?Alexa traveled at a faster rate because the slope of her line is 3/4 , which is greater than the slope of the line described by the data in Mia’s table. Alexa traveled at a faster rate because the slope of her line is4/3 , which is greater than the slope of the line described by the data in Mia’s table. Mia traveled at a faster rate because the slope of the line described by the data in her table is 1/2 , which is greater than the slope of the line on Alexa’s graph. Mia traveled at a faster rate because the slope of the line described by the data in her table is 2/1 , which is greater than the slope of the line on Alexa’s graph.

Answer:1. Alexa traveled at a faster rate because the slope of her line is [tex]\frac{3}{4}[/tex], which is greater than the slope of the line described by the data in Mia’s table.Step-by-step explanation:We know that,Slope of [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]Mia records the distance traveled over the time by the table.Taking the points (10,5) and (18,9), the slope is given by,Mia's slope = [tex]\frac{9-5}{18-10}[/tex]i.e. Mia's slope = [tex]\frac{4}{8}[/tex]i.e. Mia's slope = [tex]\frac{1}{2}[/tex]Alexa records the distance traveled over the time by the graph.Taking the points (4,3) and (8,6), the slope is given by,Alexa's slope = [tex]\frac{6-3}{8-4}[/tex]i.e. Alexa's slope = [tex]\frac{3}{4}[/tex]As, Alexa's slope = [tex]\frac{3}{4}[/tex] > [tex]\frac{1}{2}[/tex] = Mia's slope.So, the correct option is,1. Alexa traveled at a faster rate because the slope of her line is [tex]\frac{3}{4}[/tex], which is greater than the slope of the line described by the data in Mia’s table.