Is it possible to graph linear functions like h(x) = 3x + 7 without doing a table of values? If it is, how? And I know the slope is 7, which means the y-intercept is (0,7).

Answer 1

to graph linear functions we need 2 points

h(0)=3*0+7=7 first point (0,7)
h(1)=3*1+7=10 second point (1,10)

Answer 2

start with the y-intercept and plot that point.
You know the slope is 3, that is, the rise is 3 units for a run of 1, or the rise is 6 units for a run of 2 etc.

so from the y-intercept, count 3 units to the right, then 1 unit up, and mark that point.
Join the two points and you have your line.