Mr. Coleman is mapping the boundanes 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?
Since the equations given are in standard form, it is easiest to first rewrite them in slope-intercept form.
For the first equation y = -2x - 5, the slope is -2 and the y-intercept is -5.
For the second equation -2x + 4y = 12, we need to solve for y to get it in slope-intercept form:
4y = 2x + 12
y = 1/2x + 3
Now, we can graph the two lines on a coordinate grid:
1. The line y = -2x - 5 has a y-intercept of -5 and a slope of -2. Plot the point (0, -5) and then use the slope to graph the line going downward to the right.
2. The line y = 1/2x + 3 has a y-intercept of 3 and a slope of 1/2. Plot the point (0, 3) and then use the slope to graph the line going upward to the right.
The zoo's entrance is at the intersection of these two lines. You can find the coordinates by either solving the system of equations or by looking for the point of intersection on the graph.
Here is some help with the problem:
y = -2x - 5
y = 1/2x + 3
Set the two equations equal to each other:
-2x - 5 = 1/2x + 3
-5 - 3 = 1/2x + 2x
-8 = 5/2x
-16 = 5x
x = -16/5
x = -3.2
Now substitute x back into one of the equations to solve for y:
y = -2(-3.2) - 5
y = 6.4 - 5
y = 1.4
Therefore, the zoo's entrance is located at approximately (-3.2, 1.4) on the coordinate grid.