Question 73626
1.Find the slope, given the two points

(-7/5, 3/10) and (1/5, -1/2).
When given two points and asked for a slope, use the slope formula:{{{highlight(m=(y[2]-y[1])/(x[2]-x[1]))}}}, m=slope, (x1,y1) and (x2,y2) are the given points.
(x1,y1)=(-7/5,3/10) and (1/5,-1/2)
{{{m=(-1/2-3/10)/(1/5-(-7/5))}}}
{{{m=(-1/2-3/10)/(1/5+7/5)}}}
{{{m=((-1/2)(5/5)-3/10)/(1/5+7/5)}}}
{{{m=(-5/10-3/10)/(1/5+7/5)}}}
{{{m=(-8/10)/(8/5)}}}
{{{m=(-8/10)*(5/8)}}}
{{{m=-40/80}}}
{{{highlight(m=-1/2)}}}
:


2. Write the equation of the line that is parallel to 3x = 4y + 5 and passes through the point (2, -3).
In order to wirte an equation of a line, you need a point and a slope.  They gave you the point, you need to find the slope.  Parallel lines have equal slopes.  You have the equation of a parallel line.  To find its slope, put it in slope intercept form. {{{highlight(y=mx+b)}}}, m=slope, (0,b)=y-intercept.
{{{3x=4y+5}}}
{{{3x-5=4y+5-5}}}
{{{3x-5=4y}}}
{{{3x/4-5/4=4y/4}}}
{{{(3/4)x-5/4=y}}}
{{{y=(3/4)x-5/4}}}  
The coefficient of x is your slope. m=3/4
Now that you have both a slope and a point, you can use the point slope formula to find the equation of the line. {{{highlight(y-y[1]=m(x-x[1]))}}}, m=slope and (x1,y1) is the given point.
m=3/4 and (x1,y1)=(2,-3)
{{{y-(-3)=(3/4)(x-2)}}}
{{{y+3=(3/4)(x-2)}}}
{{{4(y+3)=4(3/4)(x-2)}}}
{{{4y+12=3(x-2)}}}
{{{4y+12=3x-6}}}
{{{4y+12-12=3x-6-12}}}
{{{4y=3x-18}}}*
{{{-3x+4y=3x-3x-18}}}
{{{-3x+4y=-18}}}
{{{-1(-3x+4y)=-1(-18)}}}
{{{highlight(3x-4y=18)}}}  This is the general or standard form of the equation of the line.
*If you need the slope intercept form of the equation of the line, solve for y.
{{{4y=3x-18}}}
{{{4y/4=3x/4-18/4}}}
{{{highlight(y=(3/4)x-9/2)}}}
Happy Calculating!!!!