Answer:
We can begin by finding the slope of the line 3x+4y=3 by rearranging it into slope-intercept form, y=mx+b:
4y = -3x + 3
y = (-3/4)x + 3/4
Thus, the slope of this line is -3/4.
Since the line y=mx+8 intersects the first line at a 45° angle, we know that the product of their slopes must be -1 (since the tangent of a 45° angle is 1). Therefore, we can set up the equation:
(-3/4)(m) = -1
Solving for m, we get:
m = 4/3
Therefore, the value of m that would make y=mx+8 intersect the line 3x+4y=3 at a 45° angle is 4/3.