When k < 0, y=kx+b decreases on [-3,4], so the straight line y=kx+b passes through (-3, 13), (4,8), and the equation of the straight line is solved by two-point formula.
Solution: when k > 0, y=kx+b increases on [-3,4], so the straight line y=kx+b passes through (-3,8), (4, 13).
So,
, the solution.
So the linear equation is
y=3x+ 1。
When k < 0, y=kx+b decreases on [-3,4], so the straight line y=kx+b passes through (-3, 13), (4,8),
therefore
, the solution.
So the linear equation is y =-3x+4.
To sum up, the linear equation is as follows
Y=3x+ 1, or y=-3x+4,
So the answer is
Y=3x+ 1 or y =-3x+4.
Comments: This question examines the relationship between the coefficient of the first term and the monotonicity of the first function, and solves the first equation by two-point method.