Slope (gradient) is the change in the y-axis compered to the appropriate change in the x-axis.
Slope" "-> ("change in y")/("change in x") →change in ychange in x reading left to right on the graph.
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Consider the order given in the question
Let point 1 be " "P_1->(x_1,y_1)=(7,9) P1→(x1,y1)=(7,9)
Let point 2 be " "P_2->(x_2,y_2)=(-6,7) P2→(x2,y2)=(−6,7)
color(green)("But "x_2" is less than "x_1 ")But x2 is less than x1
color(green)("and we should read left to right ( using "x")")and we should read left to right ( using x)
x_1 larr---------x_2 x1←−−−−−−−−−x2
color(red)(uarr)" direction of reading is wrong" color(red)(uarr)↑ direction of reading is wrong↑
color(red)("Highest value lowest value ")Highest value lowest value
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Change the order given in the question:
Rewrite as:
Let point 1 be " "P_1->(x_1,y_1)=(-6,7) P1→(x1,y1)=(−6,7)
Let point 2 be " "P_2->(x_2,y_2)=(7,9) P2→(x2,y2)=(7,9)
Slope" "-> ("change in y")/("change in x") =(y_2-y_1)/(x_2-x_1) =(9-7)/(7-(-6)) →change in ychange in x=y2−y1x2−x1=9−77−(−6)
Slope =2/13 =213
Positive slope means that the graph line is going upwards as you read left to right.
Note that negative slope is downwards.
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