Understanding Linear Equations and Graphs

In this video, Mr. Boskin guides students through graphing linear equations, focusing on identifying slopes and y-intercepts. He demonstrates how to graph the equation y = -4x - 1, verify its accuracy, and draw lines with given slopes and intercepts. The video also covers simplifying equations and understanding horizontal and vertical lines. The lesson concludes with a summary of key points.

What is the first step in graphing the equation y = -4x - 1?

• Identify the slope and y-intercept

• Draw a horizontal line

• Identify the x-intercept

• Plot random points

If the slope of a line is -4, how would you describe its movement?

• Down 1, over 4

• Up 1, over 4

• Down 4, over 1

• Up 4, over 1

How can you verify that a point lies on the graph of y = -4x - 1?

• Check if the point is on the x-axis

• Substitute the x-value into the equation and check the y-value

• Ensure the point is at the origin

• Draw a perpendicular line through the point

What is the equation of a line with a slope of 0 and a y-intercept of 5?

• x = 5

• y = 0x + 5

• y = 5x

• y = 5

For a line with a slope of 2 and a y-intercept of -1, what is the equation?

• y = -2x + 1

• y = 2x - 1

• y = -2x - 1

• y = 2x + 1

What is the equation of a line with a slope of -1/2 and a y-intercept of -1?

• y = 1/2x - 1

• y = -1/2x - 1

• y = -1/2x + 1

• y = 1/2x + 1

How do you simplify the equation y = 0x + 5?

• y = 5x

• y = 5

• y = x + 5

• y = 0

What is the equation of a vertical line where x = -1?

• x = -1

• x = 1

• y = -1

• y = x - 1

What is the equation of a horizontal line with a y-intercept of -2?

• y = -2x

• x = -2

• y = -2

• x = 2

Which of the following describes a vertical line?

• x = a constant

• y = mx + b

• y = a constant

• x = my + b