Question 1160169

The following table of values represents points ({{{x}}},{{{ y}}}) on the graph of a linear function. Determine the {{{y}}}-intercept of this graph.

{{{ x }}}{{{ y}}}
{{{-2 }}}{{{ 8}}} 
{{{ 1 }}} {{{2}}}
 {{{2}}}{{{  0}}}
{{{ 4}}}{{{ -4}}}

first find equation using point slope formula:


{{{y-y[1]=m(x-x[1])}}}

to find a slope, use two given points:

{{{-2 }}}{{{ 8}}} 
{{{ 1 }}} {{{2}}}

{{{m=(y[2]-y[1])/(x[2]-x[1])}}}

{{{m=(2-8)/(1-(-2))}}}

{{{m=-6/(1+2)}}}

{{{m=-6/3}}}

{{{m=-2}}}


{{{y-y[1]=m(x-x[1])}}}, plug in slope {{{m=-2}}} and coordinates of point  {{{2}}}{{{  0}}}

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

{{{y=-2x+4}}}-> your equation


to find y-intercept, set {{{x=0}}}

{{{y=-2*0+4}}}

{{{y=4}}}


y-intercept is at ({{{0}}},{{{4}}})


{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(-2,8,.12),locate(-2,8,p(-2,8)),
circle(1,2,.12),locate(1,2,p(1,2)),
circle(2,0,.12),locate(2,0.5,p(2,0)),
circle(4,-4,.12),locate(4,-4,p(4,-4)),
circle(0,4,.12),locate(0.3,4,p(0,4)),
graph( 600, 600, -10, 10, -10, 10, -2x+4)) }}}