Question 175485
X-intercept:1 means that the point (1,0) is on the line


Y-intercept:2 means that the point (0,2) is on the line



So let's find the equation of the line through the points (1,0) and (0,2)



First let's find the slope of the line through the points *[Tex \LARGE \left(1,0\right)] and *[Tex \LARGE \left(0,2\right)]



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



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



{{{m=(2)/(0-1)}}} Subtract {{{0}}} from {{{2}}} to get {{{2}}}



{{{m=(2)/(-1)}}} Subtract {{{1}}} from {{{0}}} to get {{{-1}}}



{{{m=-2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(1,0\right)] and *[Tex \LARGE \left(0,2\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-1)}}} Plug in {{{m=-2}}}, {{{x[1]=1}}}, and {{{y[1]=0}}}



{{{y=-2(x-1)}}} Simplify



{{{y=-2x+-2(-1)}}} Distribute



{{{y=-2x+2}}} Multiply




So the equation that goes through the points *[Tex \LARGE \left(1,0\right)] and *[Tex \LARGE \left(0,2\right)] is {{{y=-2x+2}}}



 Notice how the graph of {{{y=-2x+2}}} goes through the points *[Tex \LARGE \left(1,0\right)] and *[Tex \LARGE \left(0,2\right)]. So this visually verifies our answer.

 {{{drawing( 500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,-2x+2),
 circle(1,0,0.08),
 circle(1,0,0.10),
 circle(1,0,0.12),
 circle(0,2,0.08),
 circle(0,2,0.10),
 circle(0,2,0.12)
 )}}} Graph of {{{y=-2x+2}}} through the points *[Tex \LARGE \left(1,0\right)] and *[Tex \LARGE \left(0,2\right)]