How to Write the Equation of a Line in Slope-Intercept Form and Graph It: Horizontal Line Example | Summary and Q&A

TL;DR

This video explains how to solve equations, specifically converting equations to point-slope form, finding the slope and y-intercept, and graphing lines.

Key Insights

• 💁‍♂️ Converting equations to point-slope form helps identify the slope and y-intercept easily.
• 🫥 A slope of 0 indicates a horizontal line, while a non-zero slope represents a line with an inclination.
• 😃 The y-intercept is the point where the line intersects the y-axis, represented by the coordinate (0, b).

Transcript

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Questions & Answers

Q: How do you convert an equation to point-slope form?

To convert an equation to point-slope form (y = mx + b), you isolate the variable y on one side of the equation and rewrite it in that form. In this case, by adding 9 to both sides, we get y = 3.

Q: What does the slope represent in a linear equation?

The slope (m) represents the steepness or inclination of the line. In this case, the slope is 0, indicating that the line is horizontal.

Q: How do you find the y-intercept of a linear equation?

The y-intercept (b) is the point where the line intersects the y-axis. In this case, the y-intercept is 3, so the line crosses the y-axis at the point (0, 3).

Q: Can you explain why y = 3 is a horizontal line?

When the equation is in the form y = a constant, such as y = 3, it represents a horizontal line. This is because the value of y remains constant for any x value. For every value of x, y remains 3.

Summary & Key Takeaways

• The video discusses solving the equation 3y - 9 = 0 and converting it to y = mx + b form.

• It explains how to find the slope and y-intercept from the equation.

• The video demonstrates how to graph the line represented by the equation.