Final Answer:
The ordered pair that lies on the line shown in the graph is (-3, 2).
Step-by-step explanation:
To find a point on the line, let's first determine the slope of the line using the given intercepts. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. From the given intercepts, the y-intercept (0, 4) gives us b = 4.
The x-intercept (-2, 0) allows us to find the slope (m). The formula for slope (m) is (y2 - y1) / (x2 - x1). Using (-2, 0) and (0, 4), the slope (m) = (0 - 4) / (-2 - 0) = -4 / -2 = 2.
Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form: y = 2x + 4.
To find a point on this line, substitute x = -3 into the equation: y = 2 * (-3) + 4 = -6 + 4 = -2. Therefore, the point (-3, -2) satisfies the equation and lies on the line.
This point (-3, -2) fits within the specified range of the x-axis (-5 to 5) and the y-axis (-3 to -7), and it lies on the line described by the given intercepts. Therefore, the ordered pair (-3, -2) is the point that lies on the line shown in the graph.
This solution leverages the slope-intercept form of a line and the coordinates of the x and y intercepts to determine the equation of the line and then find a point on it. The calculation ensures that the point lies within the specified range and satisfies the conditions of the line equation, providing a precise answer to the question.