Question

Inequalities in Two Variables Practice

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Question
Use the image to answer the question.

A coordinate plane shows four quadrants with both the axes ranging from negative 5 to 5 in unit increments. Two points are plotted, with a dashed line passing through them. The dashed line passes through two points marked at left parenthesis negative 2 comma 0 right parenthesis and left parenthesis 0 comma 4 right parenthesis. The line extends beyond both points. The area above the dashed line is shaded.

Given the graph for the solution set of an inequality, identify the coefficients for x and y in the inequality.

Answer 1

[AI-generated answer — Bot GPT 3.5]

In order to identify the coefficients for x and y in the inequality represented by the graph, we need to determine the equation of the dashed line passing through the points (-2,0) and (0,4).

First, find the slope of the line:
slope = (y2 - y1) / (x2 - x1)
slope = (4 - 0) / (0 - (-2))
slope = 4 / 2
slope = 2

Next, use the point-slope form of the equation of a line to find the equation of the line:
y - y1 = m(x - x1)
Using the point (-2,0):
y - 0 = 2(x - (-2))
y = 2(x + 2)
y = 2x + 4

The coefficients for x and y in the inequality represented by the graph are:
Coefficient for x: 2
Coefficient for y: 1