Linear Equations and Their Properties

This lesson covers the equation of a line, focusing on standard form and graphing using intercepts. It compares different forms of equations, showing how they can represent the same line. The lesson also includes exercises on identifying parts of equations and writing equations with the same graph.

What is the standard form of a linear equation?

• y = mx + b

• ax + by = c

• x = my + b

• y = ax + c

How do you find the y-intercept of the equation 9x + 3y = 18?

• Set y to 0 and solve for x

• Set x to 0 and solve for y

• Set x to 1 and solve for y

• Set both x and y to 0

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

• (0, 6)

• (6, 0)

• (2, 0)

• (0, 2)

What do you notice about the graphs of y = 3x + 6 and 9x + 3y = 18?

• They are perpendicular

• They represent the same line

• They intersect at one point

• They are parallel lines

How can you convert y = -3x + 6 to standard form?

• Add 3x to both sides

• Subtract 6 from both sides

• Multiply by 2

• Divide by 3

In the equation 3x + y = 6, what is the coefficient of y?

• 0

• 6

• 1

• 3

What is the relationship between the equations 9x + 3y = 18 and 3x + y = 6?

• They are unrelated

• One is a multiple of the other

• They are perpendicular

• They have different slopes

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

• 3x + 4y = 14

• 3x + 2y = 14

• 6x + 4y = 14

• 6x + 2y = 7

What happens when you multiply an equation by a constant?

• The intercepts change

• The slope changes

• The graph changes

• The line remains the same

How can you simplify the equation x - 9y = 3/4?

• Subtract x from both sides

• Add 9y to both sides

• Divide by 4

• Multiply by 4