Understanding Slopes from Graphs

The video tutorial explains how to calculate the slope of a line using a graph. It introduces the concept of slope as the ratio of vertical change to horizontal change, often referred to as rise over run. The tutorial demonstrates consistent slope calculation using different points on a line, ensuring the slope remains the same. It provides examples with integer coordinates and a more challenging example with decimal coordinates, emphasizing the importance of simplifying the slope. The tutorial covers both positive and negative slopes, using blue and red lines as examples.

What is the slope of a line defined as?

• The difference between vertical and horizontal changes

• The sum of vertical and horizontal changes

• The ratio of vertical change to horizontal change

• The ratio of horizontal change to vertical change

If a line has a rise of 2 and a run of 4, what is its slope?

• 4

• 1/4

• 2

• 1/2

Why does the slope remain constant regardless of the points chosen on a line?

• Because the rise and run are always equal

• Because the ratio of rise to run is constant

• Because the points are equidistant

• Because the line is straight

What is the slope of a line if the rise is 1 and the run is 2?

• 1/4

• 1

• 2

• 1/2

When finding the slope, why is it best to use points with integer coordinates?

• To avoid fractions

• To make the graph look better

• To simplify calculations

• To ensure accuracy

What is the slope of a line if the rise is -3 and the run is 1?

• 3

• -1

• -3

• 1

How do you find the slope of a line labeled m sub 2?

• By adding the rise and run

• By calculating the ratio of rise to run

• By finding the difference between two points

• By subtracting the run from the rise

What is the simplified slope of a line with a rise of 2 and a run of 6?

• 1/6

• 2/3

• 1/2

• 1/3

In a challenging example, if the vertical change is -7.5 and the horizontal change is 6, what is the slope?

• -1

• -1.25

• -1.5

• -0.75

Why might calculating slope with decimal coordinates be more challenging?

• Decimals are harder to visualize

• Decimals are not allowed in slope calculations

• Decimals can lead to rounding errors

• Decimals require more precise calculations