Question 362570
f(-5)=-45, and f(0)=-5 means that we have the points (-5,-45) and (0,-5). The line then goes through these points.



First let's find the slope of the line through the points *[Tex \LARGE \left(-5,-45\right)] and *[Tex \LARGE \left(0,-5\right)]



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



{{{m=(-5--45)/(0--5)}}} Plug in {{{y[2]=-5}}}, {{{y[1]=-45}}}, {{{x[2]=0}}}, and {{{x[1]=-5}}}



{{{m=(40)/(0--5)}}} Subtract {{{-45}}} from {{{-5}}} to get {{{40}}}



{{{m=(40)/(5)}}} Subtract {{{-5}}} from {{{0}}} to get {{{5}}}



{{{m=8}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-5,-45\right)] and *[Tex \LARGE \left(0,-5\right)] is {{{m=8}}}



Now let's use the point slope formula:



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



{{{y--45=8(x--5)}}} Plug in {{{m=8}}}, {{{x[1]=-5}}}, and {{{y[1]=-45}}}



{{{y--45=8(x+5)}}} Rewrite {{{x--5}}} as {{{x+5}}}



{{{y+45=8(x+5)}}} Rewrite {{{y--45}}} as {{{y+45}}}



{{{y+45=8x+8(5)}}} Distribute



{{{y+45=8x+40}}} Multiply



{{{y=8x+40-45}}} Subtract 45 from both sides. 



{{{y=8x-5}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(-5,-45\right)] and *[Tex \LARGE \left(0,-5\right)] is {{{y=8x-5}}}