Exploring Negative Slopes in Graphing

This video lesson by Kirk Weiler from eMathInstruction covers unit 5, lesson 5 on slopes and negative numbers. It begins with an introduction to slopes, focusing on how negative numbers affect the slope of a line. Through various exercises, the lesson explores graphing lines with negative slopes, interpreting slope ratios, and understanding the impact of positive slopes with negative y-intercepts. The lesson emphasizes the importance of reading graphs from left to right and how slopes determine the direction of a line. The video concludes with a summary of the key concepts discussed.

What is the main topic of Unit 5 Lesson 5?

• Y-intercepts

• Slopes and negative numbers

• Equations of lines

• Proportional relationships

What happens to the y-coordinate when x equals zero in the equation y = -1/2x + 7?

• It becomes zero

• It becomes seven

• It becomes negative

• It becomes one

If the x-coordinate increases by 2 units, what happens to the y-coordinate for the line y = -1/2x + 7?

• It decreases by 1 unit

• It remains the same

• It increases by 1 unit

• It increases by 2 units

How can the slope -1/2 be interpreted in terms of changes in y and x?

• Increase in y by 1 and increase in x by 2

• Increase in y by 2 and decrease in x by 1

• Decrease in y by 1 and increase in x by 2

• Decrease in y by 2 and increase in x by 1

What does a negative slope indicate about the direction of a line?

• The line goes uphill from left to right

• The line goes downhill from left to right

• The line remains vertical

• The line remains horizontal

In the equation y = -3/4x + 6, what is the y-intercept?

• 0

• 6

• -6

• -3/4

How can the slope -2 be interpreted in terms of changes in y and x?

• Increase in y by 2 and increase in x by 1

• Decrease in y by 1 and increase in x by 2

• Decrease in y by 2 and increase in x by 1

• Increase in y by 1 and decrease in x by 2

What is the y-intercept of the line y = 4/3x - 5?

• 5

• -5

• 4/3

• 0

How can the slope 4/3 be interpreted in terms of changes in y and x?

• Decrease in y by 3 and increase in x by 4

• Increase in y by 3 and increase in x by 4

• Decrease in y by 4 and increase in x by 3

• Increase in y by 4 and increase in x by 3

What does the Greek letter Delta (Δ) represent in the context of slope?

• Product of

• Sum of

• Difference of

• Change in