Final answer:
To graph a hyperbola with the given transverse axis endpoints and slope of asymptote, follow these steps: plot the endpoints on a coordinate plane, draw the asymptotes with the given slope, and label the vertices and axis of symmetry.
Step-by-step explanation:
Step 1:
Plot the given endpoints of the transverse axis on a coordinate plane. The endpoints are (-2,-2) and (-2,7).
Step 2:
Draw the asymptotes. Since the slope of one asymptote is 4/3, this means the line will have a rise of 4 for every run of 3. Starting from one of the endpoints of the transverse axis, you can draw a line with a slope of 4/3 towards the other endpoint, extending it beyond the endpoints.
Step 3:
Label the vertices and axis of symmetry. The vertices of the hyperbola are the endpoints of the transverse axis, and the axis of symmetry is the line connecting the midpoint of the transverse axis.