8 of 148 of 14 Items 26:47 Question Mr. Coleman is mapping the boundaries of a zoo on a coordinate grid. The zoo’s headquarters are located at the origin. The equations shown below represent two boundaries of the zoo. y = −2x – 5 −2x + 4y = 12 The zoo’s entrance is located at the intersection of these two boundaries. Which coordinate grid correctly shows the two boundaries and the zoo’s entrance? Responses A AA B BB C CC D DD Skip to navigation

Question

8 of 148 of 14 Items 26:47 Question Mr. Coleman is mapping the boundaries of a zoo on a coordinate grid. The zoo’s headquarters are located at the origin. The equations shown below represent two boundaries of the zoo. y = −2x – 5 −2x + 4y = 12 The zoo’s entrance is located at the intersection of these two boundaries. Which coordinate grid correctly shows the two boundaries and the zoo’s entrance? Responses A AA B BB C CC D DD Skip to navigation

Answer 1

Based on the given equations, we can solve for the coordinates of the zoo's entrance by finding the intersection point.

First, we can rewrite the second equation in slope-intercept form (y = mx + b):

-2x + 4y = 12
=> 4y = 2x + 12
=> y = (2/4)x + 3
=> y = (1/2)x + 3

Now we can set the two equations equal to each other to find the intersection point:

-2x - 5 = (1/2)x + 3

Adding 2x and 5 to both sides:

(3/2)x = 8

Dividing both sides by (3/2):

x = 16/3

Plugging this value back into either of the equations, we can solve for y:

y = (-2)(16/3) - 5
= -32/3 - 5(3/3)
= -32/3 - 15/3
= -47/3

So, the coordinates of the zoo's entrance are (16/3, -47/3).

Now we can look at the coordinate grids shown in the responses to find the one that correctly represents the two boundaries and the zoo's entrance.