Find the equation of the line given the following..

All of these are similar...I'll do the first one and give you a hint on two more....

(-3,2) (-1,1)

The idea is to find the slope (if it's not given) and then use something called the "point-slope formula" to write the equation in the "slope-intercept form."  (We could also write the equation in "standard form,' but I prefer slope-intercept unless somebody tells me different...!!)

OK.....the slope is defined as  (change in y) / (change in x)

So, from point 1 to point 2, y changes by -1. And from point 1 to point 2, x changes by +2.

So...our slope is -1/+2  = -(1/2)

Now...we'll use one of the points (doesn't matter which) to write an equation in point-slope form. I'll choose (-1,1).

The point-slope form is given by

y - y1 = m(x - x1)     ...where m is the slope, y1 is the y coordinate of our point and x1 is the x coordinate of our point....so we have......

y - 1 = -(1/2)(x - (-1))   =

y - 1  = -1/2(x) - 1/2     ....... add 1 to both sides.....

y = -1/2(x) + 1/2

And this is in slope-intercept form...(the y intercept is the "+1/2" at the end...)

The second one is the same...and the third one has the slope already given!!

Hint......for 4 ....the y-intercept = (0, -1)

And for 5, the x intercept is (6,0)   ........!!!!