Understanding Linear Functions and Graphs

The video tutorial explains how to determine the equation of a linear function passing through two points, both graphically and algebraically. Initially, the line is graphed using a graphing tool, and the slope and Y-intercept are identified. The equation is then written in slope-intercept form. Subsequently, the algebraic method is used to verify the equation by calculating the slope using the slope formula and finding the Y-intercept through substitution.

What is the first step in determining the equation of a linear function that passes through two points?

• Graph the line using a graphing tool.

• Calculate the distance between the two points.

• Determine the equation of the line using a calculator.

• Find the midpoint of the two points.

Which tool is used to graph the line through the given points?

• Polygon tool

• Circle tool

• Rectangle tool

• Line tool

How do you determine the slope of a line graphically?

• By measuring the angle of the line.

• By counting the number of grid squares the line crosses.

• By finding the midpoint of the line.

• By calculating the change in y divided by the change in x between two points.

What is the slope of the line passing through the points (-6, 8) and (9, -7) as calculated graphically?

• 2

• 0

• -1

• 1

What formula is used to find the slope algebraically?

• Midpoint formula

• Distance formula

• Slope formula

• Quadratic formula

What is the slope of the line calculated algebraically using the points (-6, 8) and (9, -7)?

• 0

• 2

• -1

• 1

What is the y-intercept of the line found graphically?

• (0, 0)

• (0, 1)

• (0, 2)

• (0, -2)

How is the y-intercept found algebraically?

• By using the distance formula.

• By calculating the average of the y-values.

• By substituting one of the points into the equation.

• By using the midpoint formula.

What is the final equation of the line passing through the points (-6, 8) and (9, -7)?

• y = -x - 2

• y = -x + 2

• y = x - 2

• y = x + 2

Which method can be used to verify the equation of a line besides graphing?

• Using a calculator

• Using the point-slope form

• Using the quadratic formula

• Using the distance formula