What is the inequality that represents the graph?
The graph shows a 2d plane that ranges from -2 to 2 on both the x and y axis. There's a dotted line going through (0, -1) and (2, 0) with the area below it highlighted.
I semi-understand the graph, but I'm not sure how to make an inequality that represents it.
the slope of the dotted line is 1/2
the equation of the line is ... y = 1/2 x - 1
the line is dotted because it is not part of the inequality
... there is a "less than", but no "equal"
the shaded area is the solution area
y < 1/2 x - 1
To determine the inequality that represents the graph, you need to consider the properties of the graph and the highlighted area.
In this case, the graph shows a dotted line going through the points (0, -1) and (2, 0), which means the equation of the line can be found.
First, calculate the slope (m) by using the formula:
m = (change in y) / (change in x) = (0 - (-1)) / (2 - 0) = 1/2.
Now that you have the slope (m) and one point on the line (0, -1), you can use the point-slope form of a linear equation:
y - y1 = m(x - x1).
Plug in the values of m, x1, and y1 into the equation:
y - (-1) = (1/2)(x - 0).
Simplify the equation:
y + 1 = (1/2)x.
To represent the area below the line, a less than or equal to inequality is used as we want to include the highlighted region. Thus, the inequality is:
y + 1 ≤ (1/2)x.
This inequality represents the graph you described, where the shaded region is below the line.