Answer:
12. (-2, -4)
13. (6, 3)
14. y ≤ -x - 2
Step-by-step explanation:
The solution set is represented by the shaded/darker areas on the graph. The space that is lighter is not part of the solution set.
12.
Choose a point in the dark area. Find it's coordinates, which are written in brackets as (x, y).
To find the x-coordinate, start at the point you chose. Follow the grid-lines up or down to the x-axis (horizontal line with arrows labelled 'x'). The label on the x-axis is the x-coordinate.
To find the y-coordinate, go back to the point you chose. Follow the grid-lines left or right until you reach the y-axis (vertical axis). The label on the y-axis is the y-coordinate for your point.
One of the points is (-2, -4).
13.
Choose a point in the light area. Find it's coordinates the same way you found the coordinates for the other point.
One of the points is (6, 3).
14. To write the inequality represented by the graph, you need to find the equation for the line that separates the light and dark. Then decide if the the inequality is greater than or less than.
To write the equation for a line, you can use slope-intercept form, which is the equation y = mx + b.
"x" and "y" represent points on the line.
"m" represents the slope of the line, which is how steep it is.
"b" represents the y-intercept, which is where the line touches the y-axis.
When writing the equation of a line in slope-intercept form, you need to fill in a number for "m" and a number for "b".
By looking at the graph, we know that the y-intercept, "b", is -2. b = -2
To find the slope, "m", we can use the formula [tex]m = \frac{rise}{run}[/tex]. To use the formula, choose two points on the line.
Find "rise". Start at the point that is on the left side, count the number of squares up/down it takes to get to the same height as the second point. If you go up, the rise is positive. If you go down, the rise is negative.
Find "run". Count the number of squares that are between the two points horizontally. The run will only be positive.
Put the numbers for rise and run in the formula, then reduce the fraction. This is the slope.
(See diagram below) I will choose the points (-1, -1) and (1, -3).
Rise (red): I count two squares going down. Rise = -2
Run (black): I count two squares between them horizontally. Run = 2
[tex]m=\frac{rise}{run}[/tex]
[tex]m=\frac{-2}{2}[/tex] Reduce: Top and bottom can divide by 2
[tex]m=\frac{-1}{1}[/tex] A fraction over 1 does not need to be a fraction
[tex]m=-1[/tex] m = -1
When the slope is -1, we don't need to write the "1", only the negative (-).
The equation of the line using y = mx + b is y = -x - 2.
Since the area in the solution set is to the left of the line, the inequality is less than. Since the line is solid, not dotted, the solution set includes the line. It means the solution set can also be equal to the line.
Use the symbol meaning less than or equal to ≤ to replace the equal sign ( = ).
y ≤ -x - 2
