Question 146451
I'm afraid that the previous solution is completely off. The equation "3x^2 - 4" is NOT linear. 



f (0) = -4  tells us that when x=0, then y=-4. So the line goes through the point (0,-4)


f (2) = 8 tells us that when x=2, then y=8. So the line goes through the point (2,8)



So let's find the equation of the line that goes through the points (0,-4) and (2,8)






First let's find the slope through the points *[Tex \LARGE \left(0,-4\right)] and *[Tex \LARGE \left(2,8\right)]



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(8--4)/(2-0)}}} Plug in {{{y[2]=8}}}, {{{y[1]=-4}}}, {{{x[2]=2}}}, {{{x[1]=0}}}, , 



{{{m=(12)/(2-0)}}} Subtract {{{-4}}} from {{{8}}} to get {{{12}}}



{{{m=(12)/(2)}}} Subtract {{{0}}} from {{{2}}} to get {{{2}}}



{{{m=6}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(0,-4\right)] and *[Tex \LARGE \left(2,8\right)] is {{{m=6}}}



Now let's use the point slope formula:



{{{y-y[1]=m(x-x[1])}}} Start with the point slope formula



{{{y--4=6(x-0)}}} Plug in {{{m=6}}}, {{{x[1]=0}}}, and {{{y[1]=-4}}}



{{{y+4=6(x-0)}}} Rewrite {{{y--4}}} as {{{y+4}}}



{{{y+4=6x+6(-0)}}} Distribute



{{{y+4=6x+0}}} Multiply



{{{y=6x+0-4}}} Subtract 4 from both sides. 



{{{y=6x-4}}} Combine like terms. 



{{{y=6x-4}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(0,-4\right)] and *[Tex \LARGE \left(2,8\right)] is {{{y=6x-4}}}



 Notice how the graph of {{{y=6x-4}}} goes through the points *[Tex \LARGE \left(0,-4\right)] and *[Tex \LARGE \left(2,8\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,6x-4),
 circle(0,-4,0.08),
 circle(0,-4,0.10),
 circle(0,-4,0.12),
 circle(2,8,0.08),
 circle(2,8,0.10),
 circle(2,8,0.12)
 )}}} Graph of {{{y=6x-4}}} through the points *[Tex \LARGE \left(0,-4\right)] and *[Tex \LARGE \left(2,8\right)]

 

Note: as further confirmation, the graph is a straight line. So this tells us that the equation {{{y=6x-4}}} is linear.