Understanding Linear Functions and Their Equations

The video tutorial explains how to determine the equation of a linear function passing through two points, both graphically and algebraically. It begins by introducing the concept of slope-intercept form and demonstrates how to graph the line using given points. The tutorial then shows how to calculate the slope and y-intercept graphically and algebraically, ensuring the results are consistent. The lesson concludes with a verification of the equation and a summary of the methods used.

What is the slope-intercept form of a linear equation?

• y = mx + b

• y = mx^2 + b

• y = ax^2 + bx + c

• y = a/x + b

Which tool is used to graphically find the equation of a line?

• Line tool

• Polygon tool

• Circle tool

• Rectangle tool

What is the y-intercept of the line passing through the points (-4, -7) and (8, 2)?

• -7

• 2

• -4

• 0

What is the first step in finding the equation of a line graphically?

• Draw a freehand line

• Select the line tool and plot the first point

• Click on the origin

• Select the circle tool

How do you calculate the slope of a line using two points?

• Divide the change in y by the change in x

• Multiply the y-coordinates

• Subtract the x-coordinates

• Add the x-coordinates

What is the slope of the line that passes through the points (-4, -7) and (8, 2)?

• 3/4

• 4/3

• 1/2

• 2/3

Which point is used to verify the equation algebraically?

• (0, -4)

• (-4, -7)

• (8, 2)

• (0, 0)

What is the final equation of the line in slope-intercept form?

• y = 4/3x + 4

• y = 4/3x - 4

• y = 3/4x - 4

• y = 3/4x + 4

What is the purpose of verifying the slope and y-intercept algebraically?

• To change the slope

• To confirm the graphical findings

• To adjust the y-intercept

• To find a new equation

What is the significance of the y-intercept in the equation of a line?

• It is the midpoint of the line

• It is the point where the line crosses the y-axis

• It is the point where the line crosses the x-axis

• It determines the slope