Slope-intercept form from table | Linear equations and functions | 8th grade | Khan Academy | Summary and Q&A

TL;DR

The video explains how to find the equation of a line in slope-intercept form using given points.

Key Insights

• 😃 Slope-intercept form (y = mx + b) is commonly used to represent equations of lines.
• 🏙️ When the change in y between any two points is 0, the slope of the line is 0 and the equation simplifies to y = constant value.
• 💱 The slope of a line can be calculated by dividing the change in y by the change in x between two points on the line.
• 😥 To find the equation of a line, select two points, calculate the slope, and substitute one point and the slope into the slope-intercept form.

Transcript

A line goes through the following points, and the equation of that line is written in y equals mx plus b form. Also known as slope-intercept form. What is the equation of the line? So the first thing we want to think about, what is the slope of this line? What is m here? So what is our change in y for given change in x? So this is an interesting ex... Read More

Questions & Answers

Q: How do you determine the slope of a line when the change in y is always 0?

When the change in y is 0, the slope of the line is 0 because y remains constant. The equation of the line becomes y = 0x + 2 or simply y = 2.

Q: How do you find the slope when the values of y are changing?

By selecting two points on the line and calculating the change in y and change in x between those points, you can find the slope. The slope is equal to the change in y divided by the change in x.

Q: Can you explain the process of finding the equation of a line using given points?

To find the equation, choose two points on the line. Calculate the change in x and change in y between the points. The slope is the change in y divided by the change in x. Substitute one of the points and the slope into the equation y = mx + b to find the value of b.

Q: Why is it necessary to have more than two points to find the equation of a line?

It is not necessary to have more than two points; two points are sufficient to find the equation of a line. Additional points can be used to verify the accuracy of the equation.

Summary & Key Takeaways

• The video demonstrates how to find the equation of a line when the y-value is a constant, resulting in a slope of 0.

• An example is provided where the values of y are changing, leading to a non-zero slope.

• The necessary steps to calculate the slope and find the equation of the line using given points are illustrated.