Question 175487
x-intercept:2 tells us that the point (2,0) is on the line

y-intercept: -4 means that (0,-4) is on the line



So we need to find the equation of the line through the points (2,0) and (0,-4)






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



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



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



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



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



{{{m=2}}} Reduce



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



Now let's use the point slope formula:



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



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



{{{y-0=2x+2(-2)}}} Distribute



{{{y-0=2x-4}}} Multiply



{{{y=2x-4+0}}} Add 0 to both sides. 



{{{y=2x-4}}} Combine like terms. 



{{{y=2x-4}}} Simplify



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



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

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