Exploring Forms of Linear Equations

The video tutorial explains how to find the equation of a line passing through two points in different forms: point slope, slope intercept, and standard form. It begins with an introduction to these forms and their equivalence. The tutorial then provides a detailed explanation of each form, including how to calculate the slope and convert between forms using algebraic manipulation. Examples are used throughout to illustrate the concepts.

Which of the following is NOT a form of a line equation?

• Standard Form

• Quadratic Form

• Slope-Intercept Form

• Point-Slope Form

In point-slope form, what does the subscript in x₁ and y₁ represent?

• A particular coordinate on the line

• The slope of the line

• A variable that can take any value

• The y-intercept of the line

What is the point-slope form of a line passing through (-3, 6) with a slope of m?

• y - 6 = m(x + 3)

• y + 6 = m(x + 3)

• y + 6 = m(x - 3)

• y - 6 = m(x - 3)

How do you calculate the slope (m) of a line given two points?

• Change in x over change in y

• Sum of x-coordinates divided by sum of y-coordinates

• Change in y over change in x

• Product of x and y coordinates

What is the slope of the line passing through the points (-3, 6) and (6, 0)?

• 2/3

• 3/2

• -2/3

• -3/2

What is the slope-intercept form of the line with point-slope form y - 6 = -2/3(x + 3)?

• y = -2/3x - 4

• y = 2/3x - 4

• y = 2/3x + 4

• y = -2/3x + 4

In the slope-intercept form y = mx + b, what does 'b' represent?

• The x-intercept of the line

• The product of the slope and x-coordinate

• The slope of the line

• The y-intercept of the line

What is the standard form of the equation y = -2/3x + 4?

• 2x - 3y = 12

• 3x - 2y = 12

• 2x + 3y = 12

• 3x + 2y = 12

To convert from slope-intercept form to standard form, what should you do?

• Move all terms to one side and keep fractions

• Move all terms to one side and eliminate fractions

• Isolate x on one side

• Isolate y on one side

What is the result of multiplying the equation 2/3x + y = 4 by 3?

• 2x + 3y = 4

• 2x + y = 12

• 2x + 3y = 12

• 6x + 3y = 12