Exploring Linear Relationships and Equations

This video tutorial covers linear relationships, focusing on understanding and calculating slope, different forms of linear equations, and graphing techniques. It explains how to find the slope using formulas and graphing, convert between slope-intercept, point-slope, and standard forms, and verify equations using graphing tools. The tutorial also discusses key features of linear graphs, such as x-intercepts and y-intercepts, and introduces direct variation, demonstrating how to solve related problems using proportions.

What is the formula used to calculate the slope between two points?

• y2 - y1 / x2 - x1

• x2 - x1 / y2 - y1

• (x1 + y1) - (x2 + y2)

• y1 - y2 / x1 - x2

How do you convert an equation to slope-intercept form?

• Multiply each term by the coefficient of x

• Isolate y on one side of the equation

• Divide each term by the coefficient of y

• Isolate x on one side of the equation

What does an undefined slope represent in a graph?

• A vertical line

• A line with slope 1

• A horizontal line

• A line passing through the origin

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

• ax + by = c

• y - y1 = m(x - x1)

• x = my + b

• y = mx + b

What is the standard form of a linear equation?

• ax + by = c

• x = my + b

• y - y1 = m(x - x1)

• y = mx + b

What does the y-intercept represent in a graph?

• The y-coordinate where the line crosses the y-axis

• The slope of the line

• The y-coordinate where the line crosses the x-axis

• The x-coordinate where the line crosses the y-axis

What is the rate of change in a graph showing a linear relationship between x and y?

• The maximum y value minus the minimum x value

• The sum of x and y values

• The product of x and y values

• The difference in y values divided by the difference in x values

What does direct variation mean in a linear relationship?

• The relationship is represented by a horizontal line

• The relationship can be represented by a proportion

• The relationship is represented by a vertical line

• The relationship can be represented by a quadratic equation

How do you solve a proportion?

• By cross-multiplying and dividing

• By squaring both sides of the equation

• By subtracting the terms on both sides

• By adding the terms on both sides

What is the value of y when x equals 52 in a directly proportional relationship where y equals 92 when x equals 368?

• 13

• 104

• 52

• 26