graph of two infinite lines that intersect at a point. One line is solid and goes through the points (0, 2) (negative 2, 4) and is shaded in below the line. The other line is solid, and goes through the points (0, 2) (2, 0) and is shaded in below the line.
A. y less than or greater to -2x + 3
y less than or greater to x + 3
B. y greater than or equal to -2x + 3
y greater than or equal to x + 3
C. y less than or greater to -3x + 2
y less than or greater to -x + 2
D. y > -2x + 3
y > x + 3
Since both lines are y = 2-x, I'd say there's a mistake somewhere.
To determine the correct answer, we need to plot the two given lines on a graph and observe their intersection point.
Line 1:
Given the two points (0, 2) and (-2, 4), we can calculate the slope of this line using the formula: slope = (y2 - y1) / (x2 - x1).
slope = (4 - 2) / (-2 - 0) = 2 / -2 = -1.
Now that we have the slope, we can use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the point (0, 2) and the slope -1, we can write the equation of Line 1 as: y - 2 = -1(x - 0) => y - 2 = -x => y = -x + 2.
Note that since the line is solid and shaded below it, the inequality sign should be "less than or equal to."
Therefore, the equation for Line 1 is: y ≤ -x + 2.
Line 2:
Given the two points (0, 2) and (2, 0), we can calculate the slope using the same formula: slope = (y2 - y1) / (x2 - x1).
slope = (0 - 2) / (2 - 0) = -2 / 2 = -1.
Using the point (0, 2) and the slope -1, we can write the equation of Line 2 as: y - 2 = -1(x - 0) => y - 2 = -x => y = -x + 2.
Again, since the line is solid and shaded below it, the inequality sign should be "less than or equal to."
Therefore, the equation for Line 2 is: y ≤ -x + 2.
Now, let's plot these two lines on a graph:
(Note: For simplicity, I will provide a textual representation of the graph)
|
4 |
3 |
2 | (0,2)
1 |
0 __|__________________
-1 | (2,0)
-2 |
-3 |__________________
-4 -2 -1 0 1 2
Based on the graph, we can see that the two lines intersect at the point (0, 2). Looking at the shaded region below the lines, we can determine the correct inequality signs.
The correct answer is:
B. y ≥ -2x + 3 (Since the shaded region is below Line 1, the inequality sign should be "greater than or equal to.")
y ≥ x + 3 (Since the shaded region is below Line 2, the inequality sign should be "greater than or equal to.")