Answer:
The toy sinks at a rate of no more than a 1/2 meter per second ⇒ D
Step-by-step explanation:
* Lets explain the graph
- There are two lines in the graph represented two inequalities
# Red line
- The red line which is horizontal line drawn at y = -1
- The equation of any horizontal line is y = c , c is the y-intercept
∵ The red line cuts y-axis at point (0 , -1)
∴ y-intercept is -1
∴ The equation of the line is y = -1
∵ The red shaded is over the red line
∵ The red line is a sold line
∴ The inequality is y ≥ -1
# Blue line
- The line has a slope
- The equation of any line is y = mx + c , where m is the slope of the
line and c is the y-intercept
- The slope of any line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
where (x1 , y1) and (x2 , y2) are two points on the line
- Chose two point from the graph to find the slope of the line
∵ The line passes through points (2 , -1) and (-2 , 1)
∴ [tex]m=\frac{1 - (-1)}{(-2) - 2}=\frac{2}{-4}=-0.5[/tex]
- The y-intercept is the intersection between the line and the y-axis
at point (0 , c)
∵ The line passes through the origin point
∴ c = 0
∴ The equation of the line is y = -0.5x
∵ The blue line is doted line
∵ The blue shading is under the line
∴ The inequality is y < -0.5x
- The solutions of the two inequalities lie in the common shaded part
(the red and blue shaded together)
∵ The system of inequalities is used to determine the depth of a toy
in meters, in a pool depending on the time, in seconds
∵ x-axis represents the time in seconds
∵ y-axis represents the depth of the toy in meter
∵ The rate of sink of the toy is meter per second means y/x
∴ The slope of the line represents the rate of sinks of the toy
∵ the slope is -0.5
∴ The rate of toy sinks is 1/2 meter per second
∵ y < -0.5x
- The sign (<) means no more than
∴ The toy sinks at a rate of no more than a 1/2 meter per second
