Answer:
y ≤ -3/2x -2
Explanation:
You want the inequality shown on the graph that has a solid line through points (0, -2) and (2, -5).
Slope
The slope of the solid boundary line can be found from the slope equation:
m = (y2 -y1)/(x2 -x1)
m = (-5 -(-2))/(2 -0) = -3/2
Intercept
The y-intercept is the point marked on the y-axis: (0, -2).
Slope-intercept equation
The boundary line has the slope-intercept equation ...
y = mx +b . . . . . . . . where m is the slope and b is the y-intercept
y = -3/2x -2
Shading
The shading is to the left and below the boundary line, so y-values in the shaded area are less than those on the line. The inequality reflects this:
y ≤ -3/2x -2
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Additional comment
The solid boundary line is included in the solution set, so we use the ≤ symbol, instead of the < symbol that excludes the line. When the < symbol is used, the boundary line is dashed.
We use the term "y-intercept" to refer to both the ordered pair that describes the point on the y-axis, (0, -2), and the y-value in that ordered pair, -2. We understand the x-value of any point on the y-axis is 0.