Questions: Which of the following inequalities represents the graph?

Transcript text: Which of the following inequalities represents the graph?

Solution

Step 1: Find two points on the line

The line passes through the points (0, 2) and (3, -4).

Step 2: Calculate the slope

The slope of the line is given by:

m = (y2 - y1) / (x2 - x1)
m = (-4 - 2) / (3 - 0)
m = -6 / 3
m = -2

Step 3: Determine the y-intercept

The y-intercept is the point where the line crosses the y-axis, which is (0, 2) in this case. So, the y-intercept 'b' is 2.

Step 4: Write the equation of the line

Using the slope-intercept form, the equation of the line is:

y = mx + b
y = -2x + 2

Step 5: Determine the inequality

The shaded region is above the line and the line is dashed. This indicates a 'greater than' inequality. So, the inequality is:

y > -2x + 2

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