Question 72475
Find the equation, in slope intercept form, of the line that passes through the points (-7,-2) and (-4, 1).
In order to find the equation of a line you need a point and a slope.  You have two points and no slope.  Therefore, we first need to find the slope between the given two points.
When given to points and looking for a slope, use the slope formula:  {{{highlight(m=(y[2]-y[1])/(x[2]-x[1]))}}}, where m=slope and (x1,y1) and (x2,y2) are two given points.
(x1,y1)=(-7,-2) and (x2,y2)=(-4,1)
{{{m=(1-(-2))/(-4-(-7))}}}
{{{m=(1+2)/(-4+7)}}}
{{{m=3/3}}}
{{{m=1}}}
Now that we have a slope, m=1 and a point (x1,y1)=(-7,-2), we can use the point-slope formula {{{highlight(y-y[1]=m(x-x[1]))}}}, where m=slope and (x1,y1) is a given point, to find the equation of the line.
{{{y-(-2)=1(x-(-7))}}}
{{{y+2=x+7}}}
Slope intercept form is {{{highlight(y=mx+b)}}}, where m=slope and (0,b) is y-intercept.  So solve the equation for y and let x be first.
{{{y+2-2=x+7-2}}}
{{{highlight(y=x+5)}}}
Happy Calculating!!!!