Linear Equations and Their Components

The video tutorial explains how to write linear equations from word problems. It covers the basic form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. Three examples are provided: calculating distance in a race, determining plant inventory in a florist shop, and computing monthly costs for a pottery studio. Each example demonstrates how to identify the slope and y-intercept from the problem and form the corresponding linear equation.

What is the general form of a linear equation?

• y = mx^2 + b

• y = a/x

• y = ax^2 + bx + c

• y = mx + b

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

• The y-intercept

• The slope

• The x-intercept

• The constant term

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

• The slope

• The x-intercept

• The y-intercept

• The variable

If a race begins at a rate of 1.5 meters per second, what is the slope in the equation for distance?

• 0

• 1.5

• 3.0

• 2.0

In the race example, what is the y-intercept of the equation?

• 2.0

• 1.5

• 3.0

• 0

What is the equation for distance covered after T seconds in the race example?

• D = 1.5 + T

• D = 1.5T

• D = T/1.5

• D = T + 1.5

How many azalea plants arrive at the florist shop on the first day?

• 100

• 50

• 25

• 75

What is the slope in the plant shop example?

• 50

• 25

• 75

• 100

What is the y-intercept in the plant shop example?

• 75

• 50

• 25

• 0

What is the equation for the number of plants after T days?

• P = 50 + 75T

• P = 75 + 50T

• P = 50T + 75

• P = 75T + 50