Question

What is the equation Of the line, in slope-intercept form, that passes through (4,2) and (-2,-3) ?

Answer 1

Slope intercept formula:
`(y_(1)-y_(2))/(x_(1)-x_(2))`

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:

`(2-(-3))/(4-(-2))`

When there is a subtraction sign and a negative sign in a row, the operation turns into addition:

`(2+3)/(4+2)`

Which can be added and reduced to:

`(5)/(6)`

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 :)