Which linear function includes the points (-3, 1) and (-2, 4)?

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)#