Understanding Linear Functions

The video tutorial explains how to determine the equation of a linear function given two points. It starts by identifying the points from function notation, then calculates the slope using the slope formula. The tutorial proceeds to use the point-slope form to find the linear equation, and finally, it solves for Y and converts the equation into function notation, resulting in the linear function F(x) = 5/3x - 16/3.

What is the first step in determining the equation of a linear function?

• Find the slope

• Identify the y-intercept

• Calculate the midpoint

• Determine the x-intercept

If f(-1) = -7, what does this tell us about the point on the line?

• The point is (1, 7)

• The point is (-1, -7)

• The point is (1, -7)

• The point is (-1, 7)

What is the x-coordinate of the point when f(2) = -2?

• 2

• -2

• 0

• 1

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

• Add the x-coordinates and y-coordinates

• Multiply the x-coordinates by the y-coordinates

• Subtract the x-coordinates from the y-coordinates

• Divide the difference of y-coordinates by the difference of x-coordinates

What is the slope of the line passing through the points (-1, -7) and (2, -2)?

• 3/2

• 5/3

• 3/5

• 2/3

Which form is used to determine the linear equation after finding the slope?

• Standard form

• Slope-intercept form

• Point-slope form

• Quadratic form

In the point-slope form, what does the expression y - y1 represent?

• The y-intercept

• The slope

• The change in x

• The change in y

What is the final linear function derived in the video?

• f(x) = 3/5x + 16/3

• f(x) = 3/5x - 16/3

• f(x) = 5/3x - 16/3

• f(x) = 5/3x + 16/3

What is the purpose of replacing y with f(x) in the final step?

• To find the x-intercept

• To convert the equation to function notation

• To simplify the equation

• To express the equation in terms of x

What is the common denominator used to combine fractions in the final equation?

• 3

• 6

• 5

• 2