Writing Linear Equations from Word Problems

Front

What is a linear equation?

Back

A linear equation is an equation that models a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How do you identify the slope in a linear equation?

Back

The slope is the coefficient of x in the linear equation, representing the rate of change of y with respect to x.

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the value of y when x is 0, indicating where the line crosses the y-axis.

Front

How can you write a linear equation from a word problem?

Back

Identify the initial value (y-intercept) and the rate of change (slope) from the problem, then use the form y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

In the equation y = -4x + 32, what does -4 represent?

Back

-4 represents the slope, indicating that for every minute (x), the height (y) decreases by 4 feet.

Tags

CCSS.HSF.LE.B.5

Front

If an object is dropped from a height of 32 feet and falls at 4 feet per minute, how do you calculate its height after 5 minutes?

Back

Substitute x = 5 into the equation y = -4x + 32 to find y: y = -4(5) + 32 = 12 feet.

Tags

CCSS.HSF.IF.A.2

Front

What is the significance of a negative slope in a linear equation?

Back

A negative slope indicates that as x increases, y decreases, representing a downward trend.

Tags

CCSS.8.EE.B.5

Front

How do you determine the y-intercept from a word problem?

Back

The y-intercept is typically the initial value given in the problem, representing the starting point before any changes occur.

Tags

CCSS.HSF-IF.C.7A

Front

What is the slope of the equation y = -2000x + 30000?

Back

The slope is -2000, indicating that the object descends 2000 feet for every minute.

Tags

CCSS.8.EE.B.5

Front

How can you find the height of an object after a certain time if you have the linear equation?

Back

Substitute the time value into the equation to solve for the height (y).

Tags

CCSS.HSF.IF.A.2