Graphing inequalities 2 | Algebra Basics | Khan Academy

TL;DR

Graph the inequality y-4x < -3 by first converting it to slope-intercept form and then drawing a dotted line to represent the boundary before shading the region below it.

Transcript

Graph the inequality y minus 4x is less than negative 3. So the first thing we could do is we could kind of put this in mx plus b form, or slope-intercept form, but as an inequality. So we're starting with y minus 4x is less than negative 3. We can add 4x to both sides of this inequality. So let's add 4x to both sides of this inequality, and then w... Read More

Key Insights

• 💁‍♂️ The inequality y-4x < -3 is converted to slope-intercept 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.

Questions & Answers

Q: How is the inequality y-4x < -3 converted to slope-intercept form?

To convert the inequality to slope-intercept 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 y-values below the line, but not the line itself.

Q: How can the slope and y-intercept of the boundary line be determined?

The slope of the boundary line is 4 since the coefficient of x is 4. The y-intercept 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 y-4x < -3.

• The inequality is converted to slope-intercept 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.