Question 373412
write an equation in function notation for the relation graphed -
 in this case (4,0), (2,3)and (0,6). What are the steps to solve this problem?
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Use two pair of coordinates to find the slope (m) which is: m = {{{(y2-y1)/(x2-x1)}}}
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we will use the 1st and last pair, assign as follows:
x1=4; y1=0
x2=0; y2=6
:
m = {{{(6-0)/(0-4)}}} = {{{6/(-4)}}} = {{{-3/2}}} is the slope
:
Use the point/slope formula to find the equation: y - y1 = m(x- x1)
y - 0 = {{{-3/2}}}(x - 4)
y = {{{-3/2}}}x - {{{-3/2}}}(4)
y = {{{-3/2}}}x + 6 is the solution for this line
:
We can check this using the 2nd pair of coordinates, replace x with 2, find y
y = {{{-3/2}}}(2) + 6
y = -3 + 6
y = +3 which is correct
:
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Graphically
{{{ graph( 300, 200, -4, 5, -8, 8, -1.5x+6) }}}