Working on the assumption that you are talking about a straight line graph
Standard equation form is: #y=mx+c#
#x# is the independent variable
#y# is the dependant variable (its value 'depends' on what you
assign to #x#
#m# is the gradient of the line (slope)
#color(white)(XXX)#going from left to right, a positive
#color(white)(XXX)#slop is upwards and a negative slope is downwards.
#c# is a constant value and is where the line intersects the y-axis.
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#color(blue)("To find the gradient:")#
The amount of up (or down) for the amount of along. That is:
#m=("change in the y-axis")/("change in the x-axis")#
Let #(x_1 ,y_1)-> (10,3)#
Let #x_2,y_2)->(-4,12)#
so #m= (y_2-y_1)/(x_2-x_1) -> (12-3)/((-4)-10) = 9/(-14)#
#color(blue)(m=-9/14)# which is negative so the line descends from left to right
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#color(blue)("To find the constant")#
We can substitute known value for #x# and #y# to find #c#
I am choosing #color(brown)((x_1 ,y_1)-> (10,3))#
So #y_1=mx_1+c# becomes:
#color(brown)(3=color(blue)(-9/14)(10)+color(black)(c))#
#c=3+(9xx10)/14#
#color(blue)(c=3+6 3/7= 9 3/7)#
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Putting it all together:
#y=-9/14 x + 9 3/7#
