Graphing Linear Equations and Proofs

Lesson 19 of Module 4 covers the graph of a linear equation in two variables, demonstrating that it is a line. The lesson includes a formal proof for the equation y = mx + b, showing that any solution lies on the line and any point on the line is a solution. It also introduces a method for graphing linear equations using x and y intercepts, providing an alternative to using slope and y-intercept.

What is the main focus of lesson 19 in module 4?

• Exploring polynomial functions

• Studying exponential growth

• Graphing linear equations as lines

• Understanding quadratic equations

Which form of a linear equation is used in the formal proof to show it graphs as a line?

• y = a^x

• ax + by = c

• y = mx + b

• y = ax^2 + bx + c

In the specific example y = 2x + 3, what are the coordinates of point P?

• (2, 3)

• (0, 3)

• (3, 0)

• (2, 5)

What is the purpose of using point R in the proof for y = 2x + 3?

• To show it is not a solution

• To demonstrate it lies on a different line

• To find the x-intercept

• To prove it is a solution to the equation

What is the general theorem being proved for any linear equation y = mx + b?

• The graph is a circle

• The graph is a parabola

• The graph is a non-vertical line with slope m

• The graph is a vertical line

In the general proof, what is the significance of point S?

• It is a random point not on the line

• It is the y-intercept

• It is used to show any point on the line is a solution

• It is the x-intercept

What method is introduced for graphing linear equations in the final section?

• Using exponential functions

• Using polynomial division

• Using intercepts

• Using quadratic roots

How do you find the y-intercept when graphing using intercepts?

• Set y to 1

• Set x to 0

• Set y to 0

• Set x to 1

What is the x-intercept of the equation 2x + 3y = 9?

• 9

• 4.5

• 3

• 0

Which of the following is NOT a method for graphing linear equations mentioned in the lesson?

• Using an XY table

• Using intercepts

• Using the quadratic formula

• Using the slope and y-intercept