Understanding Linear Equations and Intercepts

The video tutorial covers lesson 23 on defining equations of a line. It begins with an introduction to the materials needed, followed by graphing equations using intercepts and slope-intercept form. The lesson explains how to convert equations to standard form and identifies constants. A theorem is introduced, and its parts are proven, demonstrating the relationship between different forms of equations. The video concludes with a discussion on proportions and properties, summarizing that equations representing the same line can be in different forms.

What is the y-intercept of the equation 9x + 3y = 18?

• (3, 0)

• (0, 6)

• (6, 0)

• (0, 3)

When converting y = -3x + 6 to standard form, what is the value of A?

• 3

• -3

• 1

• 0

What is the ratio of A' to A for the equations 9x + 3y = 18 and y = -3x + 6?

• 2

• 1

• 4

• 3

What is the x-intercept of the equation 4x - 8y = -24?

• (0, -6)

• (6, 0)

• (0, 6)

• (-6, 0)

How do you eliminate the fraction in y = 1/2x + 3 to convert it to standard form?

• Multiply by 3

• Divide by 2

• Divide by 3

• Multiply by 2

What is the constant ratio for the equations y = 1/2x + 3 and 4x - 8y = -24?

• 2

• 5

• 3

• 4

In the theorem, what does the constant 's' represent?

• Constant term

• Intercept

• Dilation factor

• Slope

What is the slope of the line represented by the equation 6x - 9y = 36?

• 2/3

• -2/3

• 3/2

• -3/2

What property allows us to rearrange proportions in the proof?

• Distributive Property

• Commutative Property

• Associative Property

• Identity Property

What is the defining equation of a line?

• An equation that represents a unique line

• An equation that represents a circle

• An equation with no solution

• An equation with infinite solutions