Linear Equations and Their Properties

This lesson covers the basics of linear equations in two variables, focusing on finding the slope and y-intercept. Through multiple examples, the video demonstrates how to calculate these values using different methods, including using integer points and converting between slope-intercept and standard forms. The lesson concludes with practice exercises to reinforce the concepts.

What is the general form of a linear equation in two variables?

• y = mx + b

• y = ax^2 + bx + c

• y = a/x + b

• y = ax + b

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

• Subtract the y-values and divide by the x-values

• Multiply the x-values and y-values

• Subtract the x-values and divide by the y-values

• Add the x-values and y-values

What is the next step after finding the slope to determine the equation of a line?

• Find the x-intercept

• Graph the line

• Convert to quadratic form

• Find the y-intercept

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

• Divide by the y-intercept

• Rearrange terms to get ax + by = c

• Multiply by the slope

• Add the slope to both sides

In Example 2, what is the slope of the line given the points (-4, 1) and (4, 1)?

• -1

• 1

• Undefined

• 0

What is the y-intercept of a line if the equation is y = 5x - 58?

• -58

• 58

• 0

• 5

If a line passes through the origin, what is its y-intercept?

• Undefined

• -1

• 0

• 1

What is the slope of a line that rises 1 unit and runs 3 units?

• 3/1

• 1

• 1/3

• 3

How do you determine the equation of a line given a point and a slope?

• Graph the point and draw a line

• Use the quadratic formula

• Use the point-slope form y - y1 = m(x - x1)

• Find the midpoint of the point and the origin

What is the standard form of the equation y = 1/3x?

• x + 3y = 0

• 3x + y = 0

• x - 3y = 0

• 3x - y = 0