Question 64947
  write in slope-intercept form
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1.a slope -4 and y intercept of 3/4
The slope intercept form of a line is: {{{highlight(y=mx+b)}}}, where m=slope and b=y-intercept.
In this case, m=-4 and b=3/4, so the equation is:
{{{highlight(y=-4x+3/4)}}}
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2.a line passing through (-3,-6) with slope 9/5
When given a point and a slope, we can find the equation of the line with the point-slope formula: {{{highlight(y-y1=m(x-x1))}}}, where m=slope and (x1,y1)=given point
In this case, m=9/5 and (x1,y1)=(-3,-6)
{{{y-(-6)=(9/5)(x-(-3))}}}
{{{y+6=(9/5)(x+3)}}}
{{{5(y+6)=5(9/5)(x+3)}}}
{{{5y+30=cross(5)(9/cross(5))(x+3)}}}
{{{5y+30=9(x+3)}}}
{{{5y+30=9x+27}}}
{{{5y+30-30=9x+27-30}}}
{{{5y=9x-3}}}
{{{5y/5=(9/5)x-3/5}}}
{{{highlight(y=(9/5)x-3/5)}}}
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3.line that passes through (5,2) and m=9/5
You have a point and a slope, use the point slope formula that we used for the last one:
m=9/5 and (x1,y1)=(5,2)
{{{y-2=(9/5)(x-5)}}}
{{{5(y-2)=5(9/5)(x-5)}}}
{{{5y-10=cross(5)(9/cross(5))(x-5)}}}
{{{5y-10=9(x-5)}}}
{{{5y-10=9x-45}}}
{{{5y-10+10=9x-45+10}}}
{{{5y=9x-35}}}
{{{5y/5=(9/5)x-35/5}}}
{{{highlight(y=(9/5)x-7)}}}
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Happy Calculating!!!