Linear Equations and Their Properties

This video tutorial by Mr. Holcomb covers lesson 20 on linear equations. It begins with an introduction to the concept of linear equations and proceeds to explain how to find the equation of a line using the slope and y-intercept. The tutorial includes verifying the equation by checking integer points on the line. It also covers converting the equation from slope-intercept form to standard form. The lesson concludes with practice problems to reinforce the concepts taught.

What is the general form of a linear equation?

• y = mx + b

• y = ax^2 + bx + c

• y = a/x + b

• y = ax + b/x

If a line has a slope of 2 and a y-intercept of -3, what is its equation?

• y = -2x + 3

• y = 2x + 3

• y = -2x - 3

• y = 2x - 3

How can you verify if a point lies on a given line?

• Check if the point is at the origin

• Check if the point is on the y-axis

• Check if the point is on the x-axis

• Check if the point satisfies the line's equation

What is the slope of a line that rises 3 units for every 1 unit it runs?

• 3

• 3/1

• 1/3

• 1

Which form of a linear equation is represented by Ax + By = C?

• Quadratic form

• Point-slope form

• Standard form

• Slope-intercept form

What must be true about the coefficients in the standard form of a linear equation?

• They must be integers

• They must be zero

• They must be fractions

• They must be negative

If a line has a y-intercept of 5 and a slope of 1/4, what is its equation in slope-intercept form?

• y = 4x - 5

• y = 1/4x + 5

• y = 1/4x - 5

• y = 4x + 5

How do you convert a slope-intercept equation to standard form?

• Multiply by the slope

• Add the slope to both sides

• Move the x-term to the left side

• Subtract the y-intercept from both sides

What is the standard form of the equation y = -8/5x - 7?

• 5x - 8y = 35

• 5x + 8y = 35

• 8x - 5y = 35

• 8x + 5y = 35

What is the slope of a line that descends 8 units for every 5 units it runs?

• 5/8

• -8/5

• -5/8

• 8/5