Q:

Beatrice calculated the slope between two pairs of points. She found that the slope between (-3, -2) and (1, 0) is 12.She also found that the slope between (-2, -1) and (4, 2) is 12. Beatrice concluded that all of these points are on the same line. Use the drop-down menus to complete the statements about Beatrice's conclusion.Beatrice is (correct/incorrect). All of these points (are/ are not) on the same line because the slope between (-2,-1) and (1,0) (is/ is not) equal to 1/2.

Accepted Solution

A:
Answer:The answer in the procedureStep-by-step explanation:we know thatThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] step 1Find the slope between (-3, -2) and (1, 0)[tex]m=\frac{0+2}{1+3}[/tex] [tex]m=\frac{2}{4}=\frac{1}{2}[/tex] Find the equation of the line[tex]y-y1=m(x-x1)[/tex]with m and the point (1,0)substitute[tex]y-0=\frac{1}{2}(x-1)[/tex][tex]y=\frac{1}{2}x-\frac{1}{2}[/tex]step 2Find the slope between (-2, -1) and (4, 2)[tex]m=\frac{2+1}{4+2}[/tex] [tex]m=\frac{3}{6}=\frac{1}{2}[/tex] Find the equation of the line[tex]y-y1=m(x-x1)[/tex]with m and the point (4,2)substitute[tex]y-2=\frac{1}{2}(x-4)[/tex][tex]y=\frac{1}{2}x-2+2[/tex][tex]y=\frac{1}{2}x[/tex] Compare the equation of the two linesThe two lines are parallel, because their slope is the same, but are different linesthereforeBeatrice's conclusion is incorrectAll of these points are not on the same line, because are different parallel linesThe slope between (-2,-1) and (1,0) is equal to [tex]\frac{1}{2}[/tex]