Question 178918
One definition or slope is "rise over run", a good way to think of it:
The algebra formula for slope (m): m = {{{(y2-y1)/(x2-x1)}}}
It says the same thing, y is vertical component, (rise) x is the horizontal (run)
:
What is the equation of the line passing through the points(3,7) and (11,13)? 
:
In this problem we can sign the given coordinates as follows to find the slope
x1=3, y1=7
x2=11,y2=13
:
m = {{{(13-7)/(11-3)}}} = {{{(6)/(x8)}}} reduces to {{{(3)/(4)}}} is the slope
:
Use the point/slope formula to create the equation: y-y1 = m(x-x1)
y - 7 = {{{3/4}}}(x - 3)
:
y - 7 = {{{3/4}}}x - {{{(3/4)}}}*3
:
y - 7 = {{{3/4}}}x - {{{(9/4)}}}
:
y = {{{3/4}}}x - {{{(9/4)}}} + 7
:
y = {{{3/4}}}x - {{{(9/4)}}} + {{{28/4}}}
:
y = {{{3/4}}}x + {{{(19/4)}}}; is the equation for this line
:
:
Check this by substituting the x value and ensuring that it agrees with the y value
for example using the 3, 7
y = {{{3/4}}}(3) + {{{(19/4)}}}
y = {{{9/4}}} + {{{(19/4)}}}
y = {{{28/4}}} which = 7