Which is an equation in slope-intercept form for the line passing through (–1, 5) and (5, 8)

Question

imstuck · Answer

First find the slope using the slope-intercept formula.  That is$$\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }$$Filling in these using our two points, we get $$\frac{ 8-5 }{ 5-(-1)}=\frac{ 3 }{ 6 }=\frac{ 1 }{ 2 }$$So the slope is 1/2.  Now we use the point-slope formula to find the equation.  $$y-y _{1}=m(x-x _{1})$$Pick whichever point you would like to use here.  Lets use the one with no negatives in it.  Your y1 is your y-coordinate of that point and your x1 is your x coordinate of that point, namely y = 8 and x = 5.  So let's do this.$$y-8=1/2(x-5)$$Notice that we subbed in the slope of 1/2.  Now distribute the 1/2 into the parenthesis to get $$y-8=\frac{ 1 }{ 2 }x-\frac{ 5 }{ 2 }$$Move the -8 to the other side using addition and the fact that 8 is the same thing as 16/2.$$y=\frac{ 1 }{ 2 }x-\frac{ 5 }{ 2 }+\frac{ 16 }{ 2 }$$This all simplifies down to $$y=\frac{ 1 }{ 2 }x+\frac{ 11 }{ 2 }$$And that's it in a nutshell.  And goodnight for now.  I'll return in the morning!