Graphing inequalities 2  Algebra Basics  Khan Academy  Summary and Q&A
TL;DR
Graph the inequality y4x < 3 by first converting it to slopeintercept form and then drawing a dotted line to represent the boundary before shading the region below it.
Key Insights
 💁♂️ The inequality y4x < 3 is converted to slopeintercept form, y < 4x  3, making it easier to graph.
 The boundary line y = 4x  3 is drawn as a dotted line because the inequality is strictly less than.
 The solution to the inequality is the region below the dotted line on the graph.
Transcript
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Questions & Answers
Q: How is the inequality y4x < 3 converted to slopeintercept form?
To convert the inequality to slopeintercept form, you need to isolate y on one side of the inequality. By adding 4x to both sides, you get y < 4x  3.
Q: Why is the boundary line y = 4x  3 represented as a dotted line?
The boundary line is represented as a dotted line because the inequality is strictly less than and not less than or equal to. The solution includes all the yvalues below the line, but not the line itself.
Q: How can the slope and yintercept of the boundary line be determined?
The slope of the boundary line is 4 since the coefficient of x is 4. The yintercept is 3, which is the value when x is 0. Using these values, you can plot two points or use the slope to draw the line.
Q: How can you determine if a point satisfies the inequality?
Choose a point on either side of the boundary line and substitute its coordinates into the original inequality. If the inequality is true, then the point satisfies the inequality. If it is false, then the point is not part of the solution.
Summary & Key Takeaways

The video demonstrates how to graph the inequality y4x < 3.

The inequality is converted to slopeintercept form, y < 4x  3.

A boundary line is drawn as y = 4x  3, but it is represented as a dotted line since the inequality is strictly less than and not less than or equal to.

The solution to the inequality is the region below the dotted line on the graph.