Understanding Linear Equations and Slopes

The video tutorial explains how to write equations for linear relationships using the general form y = mx + b. It covers the concepts of slope and y-intercept, demonstrating how to find these values from a graph. The tutorial includes four examples, illustrating lines with positive and negative slopes, and how to simplify slopes to whole numbers. The video concludes with tips on writing linear equations and emphasizes the importance of reducing slopes and recognizing line directions.

What is the general form of a linear equation?

• y = mx + b

• y = ax^2 + bx + c

• y = a/x + b

• y = ax + b

In the equation y = mx + b, what does 'm' represent?

• Constant

• X-intercept

• Slope

• Y-intercept

How is the slope of a line calculated?

• Sum of x and y

• Difference of x and y

• Run over rise

• Rise over run

What does the 'b' in the equation y = mx + b stand for?

• Slope

• Y-intercept

• Origin

• X-intercept

Where does the y-intercept occur on a graph?

• At the origin

• Where the line crosses the y-axis

• Where the line crosses the x-axis

• At the highest point of the line

In the first example, what is the y-intercept of the line?

• 1

• -2

• -1

• 0

What is the slope of the line in the first example?

• 1

• 3

• 2/3

• 1/3

In the second example, what is the y-intercept of the line?

• 6

• 5

• 4

• 3

What is the slope of the line in the second example?

• -3/2

• 3/2

• -2/3

• 2/3

In the third example, what is the simplified slope of the line?

• 3

• 1/2

• 2

• 1