Linear => straight line graph type function:
" "-> y=mx+c .................Equation(1)
Let point 1 be P_1->(x_1,y_1)=(-3,1)
Let point 2 be P_2->(x_2,y_2)=(-2,4)
Substitute both these ordered pairs into equation(1) giving two new equation.
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color(blue)("Determine the gradient "m)
P_1 -> 1=m(-3)+c ................................Equation(2)
P_2->4=m(-2)+c.................................Equation(3)
Equation(3) - Equation(2)
4-1=-2m+3m
color(blue)(3=m -> m=3)
color(brown)("Check: - alternative method")
Gradient ->m = ("change in up or down")/("change in along")
m=(y_2-y_1)/(x_2-x_1) = (4-1)/(-2-(-3)) =3/1=3
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color(blue)("Determine the constant (y-intercept) "c)
P_2->4=m(-2)+c
But m=3
=>4=(3)(-2)+c
4=-6+c
color(blue)(c=10)
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color(blue)("Putting it all together")
color(blue)(y=mx+c" "->" "y=3x+10)
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