ok, so actually graphing a line through two points is pretty easy. you just draw up your coordinates and then plot the two points and then draw a line thorugh them. however, they usually don't make questions that easy for us. it is usually expected when we draw a graph we should label the x and y-intercapets if any, and so, let's find those first.

now the equation of a line is of the form y = mx + b where m is the slope of the line and b is the y-intercept. we can find the x-intercept by setting y = 0 and solving for x.

to find the slope, we do the following:

given two points, (x1,y1) and (x2,y2) we can find the slope of the line through the points using the formula:

m = (y2 - y1)/(x2 - x1)

once we find the m, we can find the equation of the line by the point-slope form, which is:

y - y1 = m(x - x1)

we get the equation of the line by solving the above for y, using (x1,y1) as any one of the points we were given. so first let's get the equation of our line.

we are given (x1,y1) = (3,2) and (x2,y2) = (-2,4), so:

m = (y2 - y1)/(x2 - x1) = (4 - 2)/(-2 - 3) = 2/-5 = -2/5

so using m = -2/5 and (x1,y1) = (3,2), we have by the point-slope form:

y - y1 = m(x - x1)

=> y - 2 = (-2/5)(x - 3)

=> y - 2 = (-2/5)x + 6/5

=> y = (-2/5)x + 16/5

so now we see that our slope is -2/5 (which means our line is going from the top left to bottom right) and the y-intercept is 16/5 which is just a little bigger than 3. now let's find the x-intercept:

for x-intercept, set y = 0

=> 0 = (-2/5)x + 16/5

=> (2/5)x = 16/5

=> x = 8

so our x-intercept is 8.

now we draw our axis and label the intercepts, and draw a line through them.

the blue dots are the points that were given, the red dots are the intercepts