Linear Equations and Functions Concepts

This video tutorial covers linear functions, focusing on slope-intercept form, graph interpretation, and equation conversion to standard form. It also explores point-slope form, parallel and perpendicular lines, data correlation, and inverse functions. The tutorial provides examples and explanations to help students understand these mathematical concepts.

What is the general form of a linear equation?

• y = a/x

• y = ax^2 + bx + c

• y = mx + b

• y = mx^2 + b

If a line has a slope of 4 and a y-intercept of 5, what is its equation?

• y = 4x - 5

• y = 5x - 4

• y = 5x + 4

• y = 4x + 5

What is the equation of a line with a slope of 2 that passes through the origin?

• y = 2x - 1

• y = x + 2

• y = 2x + 1

• y = 2x

How do you determine the slope from a graph?

• Find the x-intercept

• Find the y-intercept

• Count the run over rise

• Count the rise over run

What is the equation of a line with a slope of -3 that passes through the point (0, 5)?

• y = -3x + 5

• y = 3x - 5

• y = -3x - 5

• y = 3x + 5

How do you convert an equation to standard form?

• Move all terms to one side

• Switch x and y

• Divide by the slope

• Multiply by the y-intercept

What is the point-slope form of a line?

• ax + by = c

• y = a/x

• y = mx + b

• y - y1 = m(x - x1)

What is the slope of a line parallel to y = 4x - 1?

• -1/4

• 1/4

• -4

• 4

What does a strong negative correlation in data indicate?

• As x increases, y increases

• As x increases, y decreases

• No correlation

• Vertical line

What is the inverse of the function f(x) = 2x - 4?

• f^-1(x) = 2x - 4

• f^-1(x) = (x - 4)/2

• f^-1(x) = 2x + 4

• f^-1(x) = (x + 4)/2