Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the point-slope form of linear equations, demonstrating how to write equations given a point and a slope. It also explains how to derive equations from two points using the slope formula and point-slope formula. The tutorial includes practical applications of linear equations in slope-intercept and standard forms, with examples involving real-world scenarios like cab fares and home purchases.

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

• y = m(x - x1) + b

• y - y1 = m(x - x1)

• y = mx + b

• y = mx - y1

Given the point (-1, 7) and slope -4, what is the linear equation in slope-intercept form?

• y = 4x + 3

• y = -4x + 3

• y = 4x - 3

• y = -4x - 3

How do you find the slope between two points (x1, y1) and (x2, y2)?

• (x1 - x2) / (y1 - y2)

• (y1 - y2) / (x1 - x2)

• (x2 - x1) / (y2 - y1)

• (y2 - y1) / (x2 - x1)

What is the slope of the line passing through the points (-6, 1) and (-3, 7)?

• 4

• 2

• 1

• 3

In a word problem, what does the slope typically represent?

• The starting value

• The total value

• The rate of change

• The independent variable

If a cab ride costs $4 plus $1.75 per mile, what is the equation for the total fare?

• C = 4 + 1.75m

• C = 1.75 + 4m

• C = 4m + 1.75

• C = 1.75m + 4

How much will the Joneses need to pay out of pocket if their closing costs are $6,099 and they receive $5,000 in assistance?

• $1,000

• $1,200

• $1,099

• $1,500

What is the standard form equation for the total cost if Josh buys 3 bags of potting soil and 10 bags of mulch?

• p + 10m = t

• p + m = t

• 3p + 10m = t

• 3p + m = t

If Kaylee has 17 quarters and the total value of her coins is $5.50, how many nickels does she have?

• 20

• 25

• 35

• 30

How many bags of popcorn must be sold to make at least $1,000 if 137 soft pretzels are sold?

• 100

• 110

• 118

• 120