Question 263200
"When a company spends no money on advertising, it sells 300 units" means that When x=0, then y=300 giving us the point (0,300)


"But for each additional $5000 spent, an additional 20 units are sold" adds 5000 to x=0 to get x=5000 and adds 20 to y=300 to get y=320. So we have another point (5000,320)



Now let's assume that we're dealing with a linear equation (ie a straight line). We only need to points to find the equation of this line. So let's find the equation of the line that goes through the points (0,300) and (5000,320)



First let's find the slope of the line through the points *[Tex \LARGE \left(0,300\right)] and *[Tex \LARGE \left(5000,320\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(0,300\right)]. So this means that {{{x[1]=0}}} and {{{y[1]=300}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(5000,320\right)].  So this means that {{{x[2]=5000}}} and {{{y[2]=320}}}.



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



{{{m=(320-300)/(5000-0)}}} Plug in {{{y[2]=320}}}, {{{y[1]=300}}}, {{{x[2]=5000}}}, and {{{x[1]=0}}}



{{{m=(20)/(5000-0)}}} Subtract {{{300}}} from {{{320}}} to get {{{20}}}



{{{m=(20)/(5000)}}} Subtract {{{0}}} from {{{5000}}} to get {{{5000}}}



{{{m=1/250}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(0,300\right)] and *[Tex \LARGE \left(5000,320\right)] is {{{m=1/250}}}



Now let's use the point slope formula:



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



{{{y-300=(1/250)(x-0)}}} Plug in {{{m=1/250}}}, {{{x[1]=0}}}, and {{{y[1]=300}}}



{{{y-300=(1/250)x+(1/250)(0)}}} Distribute



{{{y-300=(1/250)x+0}}} Multiply



{{{y=(1/250)x+0+300}}} Add 300 to both sides. 



{{{y=(1/250)x+300}}} Combine like terms. 



{{{y=(1/250)x+300}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(0,300\right)] and *[Tex \LARGE \left(5000,320\right)] is {{{y=(1/250)x+300}}}



Note: your book might want everything in decimal form. Since {{{1/250=0.004}}}, this means that the equation is also {{{y=0.004x+300}}}