Slope intercept formula: [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex]
x1 and y1 are taken from the first set of coordinates and x2 and y2 are taken from the second.
x1=4, x2=-2, y1=2, y2=-3
Plug these into the equation:
[tex]\frac{2-(-3)}{4-(-2)}[/tex]
When there is a subtraction sign and a negative sign in a row, the operation turns into addition:
[tex]\frac{2+3}{4+2}[/tex]
Which can be added and reduced to:
[tex]\frac{5}{6}[/tex]
So 5/6 is the slope. The equation so far in slope intercept form is: y=5/6x+b, with b being the y-intercept. To find the y-intercept, plug in one of the sets of coordinates into the x and y variables. I'll use the coordinates (4,2) for x and y respectively.
y=5/6x+b
2=5/6(4)+b
2=10/3+b
-4/3=b
Your equation is: y=5/6x-4/3
I hope this helps :)
