Linear Equations and Their Properties

In this lesson, Mr. Holcomb explores the defining equation of a line. The video covers exercises on graphing equations using intercepts, converting between standard and slope-intercept forms, and analyzing the equivalence of different equations. The lesson emphasizes understanding the relationship between equations and their graphical representations.

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

• (2, 0)

• (0, -6)

• (6, 0)

• (0, 6)

How do the graphs of 9x + 3y = 18 and y = -3x + 6 compare?

• They are perpendicular

• They intersect at one point

• They are the same line

• They are parallel lines

What is the slope of the line represented by y = 1/2x + 3?

• -2

• -1/2

• 2

• 1/2

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

• (6, 0)

• (0, -6)

• (-6, 0)

• (0, 6)

How do you convert y = 1/2x + 3 to standard form?

• Add 1/2x to both sides

• Subtract 1/2x from both sides

• Divide by 2

• Multiply by 2

Which of the following is the standard form of y = 2/3x - 4?

• 3x + 2y = 12

• 2x - 3y = 12

• 3x - 2y = 12

• 2x + 3y = 12

What is the constant term in the equation 6x - 9y = 36?

• None

• 36

• -9

• 6

If you multiply the equation 3x + 2y = 7 by 2, what is the new equation?

• 3x + 4y = 14

• 3x + 2y = 14

• 6x + 2y = 14

• 6x + 4y = 14

What happens to the graph of a line if you multiply its equation by a constant?

• The line rotates

• The line shifts up

• The line shifts down

• The line remains the same

Which of the following is an equivalent equation to x - 9y = 3/4 when multiplied by 4?

• 4x - 36y = 3

• 4x - 36y = 12

• 4x - 9y = 3

• x - 36y = 3