Graphing Linear Equations and Inequalities

The video tutorial covers graphing linear equations and inequalities. It begins with an introduction to graphing equations and identifying y-intercepts. The tutorial explains the slope-intercept form, detailing how to graph lines using slope and y-intercept. Special cases like horizontal and vertical lines are discussed. The video also covers graphing lines using standard form equations by finding x and y intercepts. Finally, it explains graphing linear inequalities, including shading regions and using solid or dashed lines based on inequality types.

Where is the y-intercept located on a graph?

• At the origin

• Where the graph crosses the x-axis

• Where the graph crosses the y-axis

• At the highest point of the graph

In the slope-intercept form y = mx + b, what does 'm' represent?

• The constant term

• The y-intercept

• The x-intercept

• The slope

If an equation is written as y = 3x - 2, what is the y-intercept?

• 0

• 3

• -2

• 1

How do you graph a line with a slope of 3/4 and a y-intercept of -3?

• Start at -3 on the y-axis, then go up 3 and right 4

• Start at 3 on the y-axis, then go up 4 and right 3

• Start at 3 on the y-axis, then go down 4 and left 3

• Start at -3 on the y-axis, then go down 3 and left 4

What type of line does the equation y = 3 represent?

• No line

• Vertical line

• Diagonal line

• Horizontal line

What does the equation x = -2 represent on a graph?

• A horizontal line at y = -2

• A vertical line at x = -2

• A point at (-2, 0)

• A diagonal line through the origin

How can you find the y-intercept of an equation written in standard form?

• By setting y to 0

• By setting x to 0

• By setting x to 1

• By setting y to 1

What is the easiest way to graph a line written in standard form?

• Use a graphing calculator

• Find the x and y intercepts

• Guess and check

• Convert it to slope-intercept form

When graphing the inequality y < 2x + 3, what type of line should be used?

• No line

• Solid line

• Dashed line

• Double line

In the inequality y ≤ 4x + 5, which region should be shaded?

• Above the line

• Below the line

• To the left of the line

• To the right of the line