Consider the graph of the linear function h(x) = –6 + x. which quadrant will the graph not go through and why?

a. quadrant i, because the slope is negative and the y-intercept is positive
b. quadrant ii, because the slope is positive and the y-intercept is negative
c. quadrant iii, because the slope is negative and the y-intercept is positive
d. quadrant iv, because the slope is positive and the y-intercept is negative

H ( x ) = - 6 + x
m = 1 ( the slope )
b = - 6 ( y - intercept )
x - intercept: 
0 = - 6 + x
x = 6 
The graph is going through Quadrants:  I, II and IV.

B ) Quadrant II, because the slope is positive and y-intercept is negative.

If we look at the function, we realize that it is a linear one. It can also be expressed in the form 
h(x) = x - 6
For simplicity.
Upon entering x = 0 to find the y-intercept (since we know that the value of x on the y intercept is 0) we see that the y-intercept is -6; thus, negative.
Next, we check the sign of the coefficient of x (which is 1 in this case) and we see that the slope is positive. Thus, when we make a quick sketch or imagine the graph, we see that the line will not pass through the second quadrant.
The answer is B.