Understanding the Equation of a Line

The video tutorial explains how to write the equation of a line with a given slope and point. It begins by introducing the concept of slope-intercept form and the need for both slope and y-intercept to form the equation. The tutorial then demonstrates how to solve for the y-intercept using a given ordered pair by substituting the x and y values into the equation. Finally, it shows how to write the complete equation of the line by combining the slope and the calculated y-intercept.

What is the first step in writing the equation of a line when given a slope and a point?

• Find the y-intercept directly.

• Substitute the slope into the equation.

• Use the point to find the slope.

• Graph the line first.

Which two components are essential to write the equation of a line?

• X-intercept and y-intercept

• Slope and x-intercept

• Slope and y-intercept

• Slope and a point

What is the role of the ordered pair in finding the equation of a line?

• To graph the line

• To calculate the x-intercept

• To find the y-intercept

• To determine the slope

How do you substitute the given point into the equation?

• Replace x and y with the given values

• Replace m with the given values

• Replace b with the given values

• Replace the entire equation with the given values

What operation is performed to isolate the y-intercept in the equation?

• Addition

• Multiplication

• Subtraction

• Division

What is the value of b after solving the equation?

• 3

• -3

• -7

• 7

What is the final form of the equation of the line?

• y = 2x + 7

• y = 1/2x - 7

• y = 1/2x + 7

• y = 2x - 7

How can the y-intercept be expressed in the final equation?

• As a positive number

• It cannot be expressed

• As a negative number

• As either positive or negative

What does the final equation represent?

• A line with a slope of 1/2 passing through the origin

• A line with a slope of 1/2 passing through the point (6, -4)

• A line with a slope of 2 passing through the point (6, -4)

• A line with a slope of 2 passing through the origin