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
