Solving Linear Equations from Word Problems

This video tutorial covers the applications of linear equations, focusing on how to write them in various forms from word problems. It explains the use of slope-intercept, standard, and point-slope forms, providing examples for each. The tutorial includes practical problems such as calculating spending over time, determining airplane weight with fuel, and budgeting for food purchases.

What is the first step when given a word problem involving linear equations?

• Write the equation in standard form

• Determine the given information

• Find the slope

• Convert the equation to slope-intercept form

When is it best to use the slope-intercept form of a linear equation?

• When given two rates for two different variables

• When given a slope and an initial amount

• When given two points

• When given a point and a slope

In point-slope form, what does the 'm' represent?

• The initial amount

• The x-intercept

• The slope or rate of change

• The y-intercept

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

• Add the slope to both sides

• Distribute the slope and simplify

• Multiply both sides by the x-value

• Subtract the y-intercept from both sides

In the example of the person spending money, what is the slope of the equation?

• 121

• 157

• 4

• -9

What is the initial value in the airplane weight problem?

• 2,575 pounds

• 56 gallons

• 6 pounds

• 2,911 pounds

How do you determine the total weight of the airplane after adding fuel?

• Add the initial weight to the product of the number of gallons and weight per gallon

• Divide the total weight by the number of gallons

• Subtract the initial weight from the total weight

• Multiply the number of gallons by the weight per gallon

In the food buying example, what form of linear equation is used?

• Quadratic form

• Point-slope form

• Slope-intercept form

• Standard form

What is the cost per pound of chicken in the food buying example?

• $75

• $2.75

• $3.50

• $12

How do you find the slope in the ticket buying example?

• Subtract the processing fee from the total cost

• Divide the difference in costs by the difference in tickets

• Add the cost of all tickets together

• Multiply the number of tickets by the cost per ticket