Question 689073
slope intercept form is y=mx+b, which is the form of your final answers.
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When given a point on the line and the slope of the line apply the point-slope formula of:  {{{y-y1 = m(x-x1)}}} where m is slope and the point gives (x1,y1)
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1.  Use point-slope formula
y - -2 = {{{2/3}}}(x-3)
y + 2 = {{{(2/3)x - 3(2/3)}}}
y = {{{(2/3)x - 2 - 2}}}
{{{highlight_green(y = (2/3)x - 4)}}} ==> this is the equation for the line
in slope-intercept form containing the point (3,-2) with a slope of {{{2/3}}}
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2.  y intercept of 5 means (0, 5).  Again use point-slope formula
y - 5 = -2(x - 0)
y - 5 = -2x
{{{highlight_green(y = -2x + 5)}}} ==> this is the slope-intercept form of the 
linear equatin to the line with a y intercept of 5 and slope of -2.
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3. Use (2, -4) and (1,8) to find slope and then apply point-slope formula
slope is {{{(-4-8)/(2-1) = -12/1 = -12}}}
y - -4 = -12(x - 2)
y + 4 = -12x + 24
{{{highlight_green(y=-12x + 20)}}}==> this is the slope-intercept form of the 
linear equation for the line containing both points.
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