first, you need your slope. this can be found by the slope formula: m = (y2 - y1)/(x2 - x1)
(3, -4) and (-4, 4)
(x1, y1) and (x2, y2)
m = (4 - -4)/(-4 - 3)
m = (8)/(-7)
so your slope is -8/7
now, to find a line through the given points, the only piece of information you're missing is your y-intercept. you just have to pick one point and plug it into slope-intercept form: y = mx + b, then solve for b
(-4) = (-8/7)(3) + b
-4 = -24/7 + b
-4/7 = b
so plug all of it into y = mx + b:
y = (-8/7)x - 4/7