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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#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)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#
#color(blue)(y=mx+c" "->" "y=3x+10)#
